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In Christianity, the outer darkness is a place referred to three times in the Gospel of Matthew (8:12, 22:13, and 25:30) into which a person may be "cast out", and where there is "weeping and gnashing of teeth". Generally, the outer darkness is thought to be hell; however, many Christians associate the outer darkness more generally as a place of separation from God or from the metaphorical "wedding banquet" that Jesus is expected to have upon his Second Coming.
New Testament 
The phrase first occurs in Jesus' comment concerning the faith of the Centurion of Capernaum:
Matthew 8:11 'I tell you, many will come from east and west and recline at table with Abraham, Isaac, and Jacob in the kingdom of heaven, 12 while the sons of the kingdom will be thrown into the outer darkness. In that place there will be weeping and gnashing of teeth.” ESV
The use of the term "outer darkness" is in Jesus' Parable of the wedding feast (also known as the parable of the marriage of the king's son). In this parable, a king arranged a wedding for his son, but the normal guests did not come; therefore, the king sent his servants to gather guests from off the street. One of these guests, however, appeared without the proper wedding attire. When the King asked, "How did you come in here without wedding clothes?" the man was speechless (Matt 22:12); therefore, the King said: "Bind him hand and foot, and throw him into the outer darkness; in that place there will be weeping and gnashing of teeth. For many are called, but few are chosen." (Matt. 22:13-14, NASB.)
The third use occurs in the Parable of the coins entrusted to servants: "'And cast the worthless servant into the outer darkness. In that place there will be weeping and gnashing of teeth.’" (Matthew 25:30).
Both Luther, who taught soul sleep till the resurrection of the dead, and Calvin, who taught the immortal soul, considered the "outer darkness" references in Matthew to refer to the last judgment. Today interpretation of these "outer darkness" verses are a subset of Protestant discussion on hell and annihilationism.
Other views include those of Zane C. Hodges who controversially suggested that it represents a place for those who make it to heaven based on their faith, but have failed to perform good works during their time on the earth.
Usage in the Latter Day Saint movement 
In the Latter Day Saint movement, "outer darkness" can refer to hell (the place where the spirits of the wicked reside after death but before the resurrection) or to the place where the sons of perdition will reside. The latter meaning is considered to be a place where the glory of God is completely absent, although it is not necessarily the place where Satan and his angels reside. Latter Day Saint beliefs on hell are connected with the movement's doctrines of the plan of salvation, the degrees of glory and the telestial kingdom.
See also 
- Gregory A. Boyd, Paul R. Eddy Across the Spectrum: Understanding Issues in Evangelical Theology pp285 2009 "For example, how can hell be a place of “outer darkness” (Matt. 22:13) if it is also a place of perpetual fire (Matt. 18:8)?"
- Hodges, Zane C. (1987), Grace in Eclipse: A Study on Eternal Rewards (2nd ed.), p. 87, ISBN 0-9607576-7-8