The Gap Theory
The Gap Theory proposes that there was a long gap in time between Genesis 1:1 and 1:2, and that the rest of Genesis 1 is effectively a re-creation story, after the creation and chaos of the gap. Most Gap Theory proponents interpret Genesis 1:2-1:31 as describing a six day creation, and would date it around six thousand years ago, as the following genealogies are thought to indicate.
Exegetically the theory is very poor, and is as incompatible with conventional science as young earth creationism, so its popularity is now greatly reduced.
Some Christians believe in a historical Adam, who was the first 'real' human - the first made in the image of God, the first with a spirit (or soul), the first moral human etc. God specially created Adam and Eve, perhaps as a new creation, or perhaps by transforming one of the prior human-like creatures, and this took place around six thousand years ago. John Stott coined the name Homo divinus for the spiritual human made in the image of God:
But my acceptance of Adam and Eve as historical is not incompatible with my belief that several forms of pre-Adamic ‘hominid’ may have existed for thousands of years previously. These hominids began to advance culturally. They made their cave drawings and buried their dead. It is conceivable that God created Adam out of one of them. You may call them homo erectus. I think you may even call some of them homo sapiens, for these are arbitrary scientific names. But Adam was the first homo divinus, if I may coin a phrase, the first man to whom may be given the Biblical designation ‘made in the image of God’. Precisely what the divine likeness was, which was stamped upon him, we do not know, for Scripture nowhere tells us. But Scripture seems to suggest that it includes rational, moral, social, and spiritual faculties which make man unlike all other creatures and like God the creator, and on account of which he was given ‘dominion’ over the lower creation. (John Stott, Understanding the Bible: Expanded Edition; 54-56)
This kind of theory is better than the Gap Theory, and is not incompatible with conventional science (though in fact it would be completely scientifically non-falsifiable.) Theologically though it has major problems: if all conventional science is to be accepted, but Adam and Eve lived only so long ago, then does that mean that peoples such as Aboriginal Australians who migrated to Australia some forty thousand years ago and then were out of communication with most of the world are not Homo divinus, that they are not actually made in the image of God?
I don't have any references on this, but I'd imagine that some extend the Homo divinus theory to say that, rather than God making a single couple, Adam and Eve, God transformed all Homo sapiens into Homo divinus at the same time. This solves the problem I just raised, but then loses the main benefit of Stott's Homo divinus theory: having a historical Adam and a historical fall.
One view that has some similarities to the previous one is Progressive creationism, which says that through the ages God has directly and specially created each life form, including humans. This view accepts the conventional age of the earth and fossils dates, but rejects evolution. Instead each kind of creature was created as is by God, and has remained the same since that time. As with Homo divinus, progressive creationists would accept that there were homonids before modern Homo sapiens. Seeing as there appears to be evidence of Homo sapiens long before six thousand years ago, many progressive creationists would probably say that God created them before that time, but some might say that God created them when the Biblical genealogies would indicate.