Jesus died, and his spirit (which is also God), went to wherever it is our souls rest/hangout before judgement day, for 3 days he was there, and then he came back to the physical world (Jesus), to give one last message, and then he ascended to Heaven.
From my understanding, when we die, we don't go to Heaven (or Hell) at first. Our spirits rest or hang out at some place until Judgement day. Then God calls every person that died, and is still living, (their spirit), and judges them accordingly. Then, for the believers, he makes a New Jerusalem, or a new earth, and our new bodies as believers (whether it's physical in a sense, or our spiritual body) live in this new earth. Some say that New Jerusalem is Heaven, but to my belief, it is a whole new place that God creates for us, and we live how Adam was supposed to live, but with no more temptation (because Satan is out of hte picture). Now, we probably can visit Heaven (which New Jerusalem might be at the gates of Heaven), but our home is on New Jerusalem.
Elijah (Elisha?) is the one taken before his death. He asked God to take him because he was tired of this worldly life, and God answered him with a yes. So he took Elijah, before his physical death.
And then there will be the rapture, where all those living here on the Earth that are believers during the tribulation or before it (it doesn't specify when on a time table) will be taken up, but first the spirits of the dead will be taken. God might have us wait in Heaven with him til Judgement day, or he might take us to wait somewhere else, I couldn't tell ya.