After believers die, they go to heaven. Their bodies decay on earth. But their spirits are in heaven.
There are many Bible verses that support this.
The thief on the cross who ended up believing in Jesus went to heaven after he died.
"And he was saying, 'Jesus, remember me when You come in Your kingdom!' And He said to him, 'Truly I say to you, today you shall be with Me in Paradise.'" (Luke 23:42-43)
Jesus didn't say he would go to Paradise at a later time, but he would enjoy Paradise that same day.
Stephen, the first Christian martyr, went to heaven immediately after his death.
"But being full of the Holy Spirit, he gazed intently into heaven and saw the glory of God, and Jesus standing at the right hand of God...They went on stoning Stephen as he called on the Lord and said, 'Lord Jesus, receive my spirit!' Then falling on his knees, he cried out with a loud voice, 'Lord, do not hold this sin against them!' Having said this, he fell asleep." (Acts 7:55, 59-60)
So Stephen's body fell asleep (euphemism for died), but his spirit went to Jesus in heaven. Stephen said, "Lord Jesus, receive my spirit!" (Acts 7:59). This means when he died, Jesus in heaven received his spirit.
The Bible also says:
"Therefore, being always of good courage, and knowing that while we are at home in the body we are absent from the Lord— for we walk by faith, not by sight— we are of good courage, I say, and prefer rather to be absent from the body and to be at home with the Lord." (2 Corinthians 5:6-8)
If we are in our bodies, we are absent from the Lord Jesus. But if we are absent from our bodies, then it means we have died and gone to heaven to be with the Lord Jesus.
The Bible describes heaven as a place where God dwells with the spirits of the righteous made perfect:
"But you have come to Mount Zion and to the city of the living God, the heavenly Jerusalem, and to myriads of angels, to the general assembly and church of the firstborn who are enrolled in heaven, and to God, the Judge of all, and to the spirits of the righteous made perfect, and to Jesus, the mediator of a new covenant, and to the sprinkled blood, which speaks better than the blood of Abel." (Hebrews 12:22-24)
So the spirits of the righteous made perfect (saints who died) are in heaven.
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Believers will receive new resurrection bodies after the rapture of the church.
"Behold, I tell you a mystery; we will not all sleep, but we will all be changed, in a moment, in the twinkling of an eye, at the last trumpet; for the trumpet will sound, and the dead will be raised imperishable, and we will be changed. For this perishable must put on the imperishable, and this mortal must put on immortality." (1 Corinthians 15:51-53)
The bodies we as believers will receive will be incorruptible and immortal.
They will not be like our original bodies. The Bible explains:
"That which you sow does not come to life unless it dies; and that which you sow, you do not sow the body which is to be, but a bare grain, perhaps of wheat or of something else. But God gives it a body just as He wished, and to each of the seeds a body of its own." (1 Corinthians 15:36-38)
So from this analogy, our new bodies will be as different from us currently as wheat is different from its seed.
Just as wheat seed makes wheat, so your current body will be the starting point God uses to create your new heavenly body.
"All flesh is not the same flesh, but there is one flesh of men, and another flesh of beasts, and another flesh of birds, and another of fish. There are also heavenly bodies and earthly bodies, but the glory of the heavenly is one, and the glory of the earthly is another. There is one glory of the sun, and another glory of the moon, and another glory of the stars; for star differs from star in glory.
So also is the resurrection of the dead. It is sown a perishable body, it is raised an imperishable body; it is sown in dishonor, it is raised in glory; it is sown in weakness, it is raised in power; it is sown a natural body, it is raised a spiritual body. If there is a natural body, there is also a spiritual body." (1 Corinthians 15:39-44)
If we die before the rapture, our spirits in heaven will put on spiritual bodies when the time comes. This is called the resurrection of the dead.
But if we are raptured by Jesus, then we will not go through death, and our natural bodies will change to spiritual bodies in the twinkling of an eye (1 Corinthians 15:51-52).