Eschatology is the theological study of "the last things". More specifically, it refers to heaven, hell, (and purgatory), and also the end of the world. Although reputed private revelations have helped shape popular eschatological concepts among many Catholics, what we know for certain about the last things come from Catholic teaching, as derived from Scripture and Tradition.
The first of the last things is death. Immediately following the death of the body, the soul is judged in what is called the "particular judgement" (Heb. 9:27; CCC 1021), judgement being the second of the last things. What kind of judgement is this? The soul is judged as meriting heaven or meriting hell, the third and the fourth of the last things. Those who are condemned to hell go immediately there. Souls judged worthy of heaven may go directly there, or may have to suffer in purgatory before arriving at their final destination in heaven. So what exactly are heaven, hell, and purgatory, and who goes there?
Heaven is not only a place, but also the state, of perfect happiness. The greatest joy of heaven is the "Beatific Vision", or seeing God "face-to-face" (1 Cor. 13:12), for all eternity (Rev. 14:11). Heaven is also the place where Jesus, Mary, and the angels and saints reside, and souls who go to heaven enjoy their companionship forever. The degree of happiness varies from soul to soul, based on each soul's merits, but each is perfectly happy. It is comparable to different sizes of glasses, but each glass being equally full. Since the will of those in heaven is completely fixed on God, there is no way they can turn away from God and lose eternal life. Who goes to heaven? Everyone who dies in the state of grace goes to heaven (CCC 1023), either immediately of after passing through purgatory.
Hell is the place and the state of everlasting punishment. The greatest pain of hell is the pain of loss, knowing that one will be eternally separated from God (CCC 1035). The lesser pain is the pain of sense, which has traditionally been identified as fire (Mark 9:48), although it is a fire unlike what we are familiar with on earth. The degree of punishment differs from soul to soul, based on their aversion from God. Who goes to hell? Those who die in a state of unrepentant mortal sin go to hell (CCC 1033). It must be stated that God does not condemn anyone to hell; rather, people make a free choice to go there by turning away from God.
Purgatory is quite appropriately called "the final purification" (CCC 1030-1032). Even after one's sins are forgiven, people are required to expiate their sins through penance, so as to satisfy for what is called "temporal punishment". Those who die in the state of grace, but with venial sins on their souls, or who have not expiated their sins fully, must go to purgatory, where they suffer to make satisfaction for their sins, or where self-love is transformed into love for God. Those on earth can help the souls in purgatory by praying for them, offering the Mass for them, and by applying indulgences to them, so that their stay in purgatory will be shortened.
Besides the particular judgement, there is another judgement, which is called the "general judgement". Towards the end of time, there will be a great Tribulation (Matt. 24; Luke 21), the "Antichrist" will come, and will lead a great apostasy (CCC 675). He will be a great enemy of the Catholic faith, and will back his claim to be God through mock-miracles (Matt. 24:5,11,24; 2 Thess. 2; 1 John 2:18,22, 4:3; Rev. 13). The Antichrist will be destroyed by Christ and His Second Coming (Acts 1:11), after which will come the end of the world. Following this, the general judgement will take place (CCC 678). This is where the deeds of all people will be revealed to all (Luke 12:3), and each soul's eternal fate is revealed to all, whether it be heaven or hell, based on their deeds (Matt. 25:31-46). At this time, the bodies of all who have died will rise and join their souls for all eternity (1 Cor. 15), to share in the rewards or punishments of the souls. When will all this take place? "But of that day or that hour no one knows, not even the angels in heaven, nor the Son, but only the Father" (Mark 13:32). The end will come like a "thief in the night" (Matt. 24:43). Therefore, we must always be prepared for death and judgement, because the end of time, or the end of our lives, may come at any time.