The last judgment takes place outside of time, after the passing away of the old earth and the old heaven, when fire comes down from heaven to destroy the armies besieging the city that God loves (see Rev 20:7-15). The earth will be destroyed by fire before the last judgment (see 2Pet 3), during which every person will be resurrected in the flesh and either consinged to lake of fire or ascend to the glory of the beatific vision. Those who die outside of God’s grace either descend into hell or enter into the state of purgatory (depending on the level of sin and repentence at the moment of death). Those who are in the state of purgatory will all enter into the beatific vision after a purification through fire, since purgatory has only one exit and that leads into the glory of eternal life with Christ. There is also some dispute in Catholic theology as to the extent of hell, which is linked to theodicy and the philosophical “problem of evil”. See Hans Ur Von Balthasar’s Dare We Hope “That All Men Be Saved”? or an excellent overview of Cardinal Avery Dulles article The Population of Hell which can be found
here.
The Church also teaches that each person is met with a particular judgment at the moment of death, before the general resurrection which takes place after the dissolution of the cosmos.
The Second Coming of Christ or appearance of the Son of Man at the end-time will not be accompanied by a rapture, but rather it is a last sign of hope calling mankind to repentence before the final tribulation and destruction of the world by fire. In addition to the material listed above by Hahn, Thigpen, Olsen etc, the excellent new book
Unveiling the Apocalypse by Emmett O’Regan details a Catholic view of end-times theology.