Where does a Christian go when they die? Where does a non-Christian go? I know about heaven and hell, but could you explain what details the Bible gives about this?

Let's begin by looking at the following passage:
There was a certain rich man, which was clothed in purple and fine linen, and fared sumptuously every day: And there was a certain beggar named Lazarus, which was laid at his gate, full of sores, And desiring to be fed with the crumbs which fell from the rich man's table: moreover the dogs came and licked his sores.

And it came to pass, that the beggar died, and was carried by the angels into Abraham's bosom: The rich man also died, and was buried; And in hell he lift up his eyes, being in torments, and seeth Abraham afar off, and Lazarus in his bosom. And he cried and said, "Father Abraham, have mercy on me, and send Lazarus, that he may dip the tip of his finger in water, and cool my tongue; for I am tormented in this flame."

But Abraham said, "Son, remember that thou in thy lifetime receivedst thy good things, and likewise Lazarus evil things: but now he is comforted, and thou art tormented. And beside all this, between us and you there is a great gulf fixed: so that they which would pass from hence to you cannot; neither can they pass to us, that would come from thence."
(Luke 16:19-26 KJV)
Before Jesus died and was resurrected, Old Testament saints, and those who weren't in covenant with God, went to places that were close to one another. The sinners were in hell or Hades, and the just people were in a nearby place that was separated from Hades by a great gulf. After Jesus arose from the dead, He led all those saints, Abraham and others, into Heaven (Eph. 4:8-10).

The sinners stayed in Hades. Now, according to the Bible, those who reject Christ will still go to Hades, and await the great White Throne Judgment, and Christians go to Heaven to be with the Lord when they die (Phil. 1:21-24).

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