Hell, Hades, Sheol, and Gehenna
Eternal Punishment in Christianity
In the Christian religion, hell is the place where unrepentant sinners go after this life. The Bible describes hell as eternal (Jude 7, 12-13) and punitive (e.g. Matt. 23:32, 2 Pet. 2:4). Hell is further described as a place of fire (e.g. Matt. 25:41), although there isn't consensus among Christians as to whether that imagery is intended to be literal or figurative. According to Jesus Christ, hell was originally intended for the Satan and demons (cf. Matt. 25:41).
According to a Gallup Poll, 70% of Americans believe in hell. Belief in hell is highest among regular churchgoers: 92% of those who attend church weekly believe in hell, as do 74% of those who attend nearly weekly.
Even among those who believe in hell, there are differences in how they interpret the biblical descriptions. Some believe that in hell people will literally burn forever. Others believe people will literally burn for a certain period of time, and then cease to exist (this view is called "annihilationism"). Still others believe that although hell is a place of punishment, the descriptions of fire are simply imagery meant to convey judgment.
Hell in the Old and New Testaments
In popular English Bible translations, the word "hell" is used to translate the Hebrew word Sheol, its Greek equivalent Hades, and another Greek word, Gehenna. Since most scholars believe the biblical authors are describing the same location in the afterlife with these terms, most English Bible translations opt to translate each one with the word "hell." There is, however, insight to be gleaned from understanding each of the terms individually, because they each have nuances and convey different aspects to the nature of hell.
Sheol and Hades
In the Old Testament, Sheol, which is also sometimes translated "grave" or "pit," denotes the underworld or the place of departed spirits. It is important to understand that the word Sheol doesn't always refer to hell, but sometimes simply refers to "the grave" (i.e. death). It is in this sense that the righteous are described as going to Sheol (e.g. Psalm 16:10, 30:3, and Isaiah 38:10). Yet other times, Sheol refers to the eternal destination of the wicked (e.g. Num. 16:33, Job 24:19, Psalm 9:17). Context determines the meaning of Sheol.
The New Testament equivalent of Sheol is the Greek term "Hades," which many popular English Bibles translate as "hell." Jesus uses the word hades to describe a place of eternal punishment (Matt. 11:23). In other contexts, it refers to "the grave" or the location a person goes prior to resurrection (e.g. Acts 2:27), either for eternal judgment or eternal paradise.
Gehenna (i.e. "the Valley of Hinnom") is the Greek translation of a Hebrew word, which refers to an actual place on earth. The identity of Hinnom is not known for certain, but scholars have suggested it is an area southwest of Jerusalem near the Cedron. Gehenna is mentioned in Joshua 15:8 and 18:16, and in 2 Kings, it is described as a place of human sacrifice (16:3, 21:6; cf. 23:13-14) that was polluted (23:10-12).
In later Jewish thought, Gehenna was a place of punishment for apostates and other great sinners (e.g., 1 Enoch 27:2, 90:26; 2 Esdras 7:36-38). A statement dating to 1200 AD that fires were continually kept burning in the Valley of Hinnom is generally regarded as reliable, although no earlier reference has yet been found. 
Hell in the Old Testament
The idea of hell (as understood in Christianity) is only hinted at in the Old Testament. A possible mention hell in the Old Testament is this prophecy about the end times:
"Multitudes who sleep in the dust of the earth will awake: some to everlasting life, others to shame and everlasting contempt." (Daniel 12:2, NIV)
Another notable passage that likely contributes to Christian imagery of hell is Isaiah 66:24, which also refers to the end times:
"And they will go out and look upon the dead bodies of those who rebelled against me; their worm will not die, nor will their fire be quenched, and they will be loathsome to all mankind." (NIV)
Other passages that speak of the afterlife seem to indicate extinction of the soul after death (see, e.g., Ecclesiastes 9:10). Rabbis have generally the taught the existence of a hell-like place for the unrighteous, but many Jews, both historical and modern, do not believe in hell or an afterlife. (See Jewish Beliefs: Afterlife.)
Hell in the New Testament
In the New Testament, the notion of hell is more clearly expressed, but still not in a systematic way. In many cases, "death" and "destruction" are the only mentioned penalties for rejecting God (e.g., Matthew 7:13, John 3:16, Acts 4:12, Romans 6:23, 2 Thessalonians 1:9, James 1:15). New Testament passages that have suggested eternal torment to Christians include the following:
"Anyone who says, 'You fool!' will be in danger of the fire of hell." (Matthew 5:22, quoting Jesus)
"And if your right hand causes you to sin, cut it off and throw it away. It is better for you to lose one part of your body than for your whole body to go into hell." (Matthew 5:29, quoting Jesus; see parallel passage in Mark 9:44, which adds, "where the fire never goes out.")
"Do not be afraid of those who kill the body but cannot kill the soul. Rather, be afraid of the One who can destroy both soul and body in hell." (Matthew 10:28, quoting Jesus)
"As the weeds are pulled up and burned in the fire, so it will be at the end of the age. The Son of Man will send out his angels, and they will weed out of his kingdom everything that causes sin and all who do evil. They will throw them into the fiery furnace, where there will be weeping and gnashing of teeth." (Matthew 13:40-42, quoting Jesus)
"Throw that worthless servant outside, into the darkness, where there will be weeping and gnashing of teeth." (Parable of the Talents, Matthew 25:30)
"Then he [the King] will say to those on his left, 'Depart from me, you who are cursed, into the eternal fire prepared for the devil and his angels." (Parable of the Sheep and the Goats, Matthew 25:41)
"The tongue also is a fire, a world of evil among the parts of the body. It corrupts the whole person, sets the whole course of his life on fire, and is itself set on fire by hell." (James 3:6)
"The sea gave up the dead that were in it, and death and Hades gave up the dead that were in them, and each person was judged according to what he had done. Then death and Hades were thrown into the lake of fire. The lake of fire is the second death. If anyone's name was not found written in the book of life, he was thrown into the lake of fire." (Revelation 20:13-15)
"The cowardly, the unbelieving, the vile...the idolaters and all liars - their place will be in the fiery lake of burning sulpher. This is the second death." (Revelation 21:8)
The Doctrine of Hell in the Church Fathers
In the church fathers (post-New-Testament Christian leaders and theologians), the doctrine of hell is understood as as a place of eternal torment, which is generally seen as physical in nature: 
"The way of darkness is crooked, and it is full of cursing. It is the way of eternal death with punishment." (Pseudo-Barnabas, c. 70-130 AD)
"You should fear what is truly death, which is reserved for those who will be condemned to the eternal fire. It will afflict those who are committed to it even to the end." (Letter to Diognetus, c. 125-200)
"[The martyrs] despised all the torments of this world, redeeming themselves from eternal punishment by the suffering of a single hour.... For they kept before their view escape from that fire which is eternal and will never be quenched." (Martyrdom of Polycarp, c. 135)
"Sinners will be consumed because they sinned and did not repent." (Shepherd of Hermas, c. 150)
"Those who have not known God and do evil are condemned to death. However, those who have known God and have seen his mighty works, but still continue in evil, will be chastised doubly, and will die forever." (Shepherd of Hermas, c. 150)
"We believe...that every man will suffer punishment in eternal fire according to the merits of his deed. ... Sensation remains to all who have ever lived, and eternal punishment is laid up." (Justin Martyr, c. 160)
"Hell [Gehenna] is a place where those who have lived wickedly are to be punished." (Justin Martyr, c. 160)
"Some are sent to be punished unceasingly into judgment and condemnation of fire." (Justin Martyr, c. 160)
"We who are now easily susceptible to death, will afterwards receive immortality with either enjoyment or with pain." (Tatian, c. 160)
"We are persuaded that when we are removed from the present life we will live another life, better than the present one...or, if they fall with the rest, they will endure a worse life, one in fire. For God has not made us as sheep or beasts of burden, who are mere by-products. For animals perish and are annihilated. On these grounds, it is not likely that we would wish to do evil." (Athenagoras, c. 175)
"To the unbelieving and despisers...there will be anger and wrath, tribulation and anguish. At the end, everlasting fire will possess such men." (Theophilus, c. 180)
"Eternal fire is prepared for sinners. The Lord has plainly declared this and the rest of the Scriptures demonstrate it." (Irenaeus, c. 180)
"All souls are immortal, even those of the wicked. Yet, it would be better for them if they were not deathless. For they are punished with the endless vengeance of quenchless fire. Since they do not die, it is impossible for them to have an end put to their misery." (Clement of Alexandria, c. 195; from a post-Nicene manuscript fragment)
"We [Christians] alone make a real effort to attain a blameless life. We do this under the influence of... the magnitude of the threatened torment. For it is not merely long-enduring; rather, it is everlasting." (Tertullian, c. 197)
"Gehenna... is a reservoir of secret fire under the earth for purposes of punishment." (Tertullian, c. 197)
"There is neither limit nor termination of these torments. There, the intelligent fire burns the limbs and restores them. It feeds on them and nourishes them. ... However, no one except a profane man hesitates to believe that those who do not know God are deservedly tormented." (Mark Minucius Felix, c. 200)
Modern Christian Views of Hell
In many modern Christian views, hell is seen as a logical extension of the free will of mankind to reject God's gracious advances. Some modern Christians question hell's eternal nature in favor of some form of universalism (i.e. that all are saved in the end) or annihilationism (i.e. that wicked souls are eventually destroyed).
The following is a sampling of the positions of various Christian denominations on the issue of hell.
It is impossible to describe the glory and splendor of heaven and the terror and torment of hell. Whether taken literally or figuratively, the meaning is the same: Hell is a place where one will experience total separation from God; heaven enjoys the total presence of God. Knowing that this is the horrible end awaiting the wicked, the Assemblies of God is strongly motivated to win the lost before it is too late. (Assemblies of God)
To die in mortal sin without repenting and accepting God's merciful love means remaining separated from him for ever by our own free choice. This state of definitive self- exclusion from communion with God and the blessed is called "hell." (Catechism of the Catholic Church)
The statement of Christ in Matthew 25, and elsewhere, are taken at face value. It is believed that after death each man must come before God in judgment and that he will be judged according to the deeds done while he lived (Hebrews 9:27). After judgment is pronounced he will spend eternity either in heaven or hell. (Churches of Christ)
We believe that glorious and everlasting life is assured to all who savingly believe in, and obediently follow, Jesus Christ our Lord; and that the finally impenitent shall suffer eternally in hell. (Church of the Nazarene)
This hope for the final salvation of humanity and the eternal universal restitution of all things in heaven and on earth ... is drawn from the unlimited promise of the Gospel and the magnitude of God's grace made known to the world through Christ. (Evangelical Lutheran Church of America)
We believe in the bodily resurrection of the dead; of the believer to everlasting blessedness and joy with the Lord; of the unbeliever to judgment and everlasting conscious punishment. (Evangelical Free Church of America)
The moral progress of the soul, either for better or for worse, ends at the very moment of the separation of the body and soul; at that very moment the definite destiny of the soul in the everlasting life is decided. ... The Orthodox Church believes that at this moment the soul of the dead person begins to enjoy ... the life in Paradise or to undergo the life in Hell. There is no way of repentance, no way of escape, no reincarnation and no help from the outside world. (Greek Orthodox Archdiocese of America)
Common arguments for an eternal hell
Among the common arguments advanced for the existence of an eternal hell are these:
- Words and pictures in the New Testament imply finality.
- The doctrine of hell has been believed for a long time by eminent theologians.
- Offers of pardon are restricted to the present world.
- The judgment occurs at the close of the redemptive era, and hence is final.
- Character tends to final permanence.
- The conscience expects and demands retribution in another life. 
Common arguments against an eternal hell
Commonly presented arguments against the existence of an eternal hell include:
- Words and pictures in the New Testament imply death and destruction (i.e., annihilation).
- "Eternal punishment" can refer to results that are eternal, not an eternal process.
- Vindictive justice is not compatible with the God of love and compassion revealed in the New Testament.
- The punishment does not fit the crime (i.e. non-eternal sin and disbelief). 
- Hell contradicts the Christian assertion of the final victory of God over evil. 
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- "Hell." F.L. Cross and E.A. Livingstone, eds., The Oxford Dictionary of the Christian Church, 3rd ed. (Oxford UP, 1997), p. 748-49.
- "hell." Encyclopędia Britannica. 2005. Encyclopędia Britannica Premium Service. 17 Jan. 2005 <http://www.britannica.com/eb/article?tocId=9039897>.
- "Sheol." The Oxford Dictionary of the Christian Church, 3rd ed., p. 1494.
- "Gehenna." The Oxford Dictionary of the Christian Church, 3rd ed., p. 657.
- "Eternal Punishments and Rewards." David W. Bercot, ed., A Dictionary of Early Christian Beliefs (Hendrickson, 1998), pp. 241-43.
- Joseph Hontheim, "Hell." The Catholic Encyclopedia, Vol. XIV (Robert Appleton, 1910). <http://www.newadvent.org/cathen/07207a.htm>
- "Future Punishment." The New Schaff-Herzog Encyclopedia of Religious Knowledge, Vol. IV, p. 415. <http://www.ccel.org/php/disp.php3?a=schaff&b=encyc04&p=415>.
- Ibid. and Timothy R. Phillips, "Hell." Walter A. Elwell, ed., Baker's Evangelical Dictionary of Biblical Theology (Baker Books, 1996). <http://bible.crosswalk.com/Dictionaries/BakersEvangelicalDictionary/bed.cgi?number=T336>
- Alister McGrath, Christian Theology: An Introduction, 2nd ed. (Blackwell, 1997), pp. 553-54.