For those who have committed unpardonable sins, there is no escape from the torments of Hell. These are the people to whom the gospel was preached, who understood the Plan of Salvation, who were baptized and received the Holy Ghost, but then chose to deny Jesus Christ. Such is the case for many apostates of the Church. They are beyond hope of salvation, and will remain in a state of torture and misery for all eternity.
But what about those being tortured in Hell who never even had the opportunity to hear the gospel? Only a vindictive God would allow their torture to continue without end. Starting at the end of Jesus's mortal life, Heavenly Father has allowed missionaries from Paradise to visit Hell and preach to the spirits held captive there in chains, giving all his children a chance to accept the gospel, and make spiritual progress.
If someone is guilty of great sins, they will be punished for them. But if they repent, accept the gospel, and have the necessary temporal rituals performed by living members of the Church on their behalf, they can reach a stage at which the prison doors will open for them, and they will exit Hell and be welcomed with great rejoicing into Paradise.
Those who have not committed unpardonable sins, but who are preached to by missionaries and choose not to repent or accept the gospel of Jesus will remain in misery in hell until the time of the Resurrection at the end of Jesus's thousand-year reign on Earth after his Second Coming. Then they will be assigned in the Final Judgement to the lowest of the three kingdoms of heaven.
Also from the creator of The Brick Book of Mormon: