Evolutionary Creationism (EC), formerly known as Theistic Evolution, accepts the modern theory of evolution. Just as Christians hold to many different beliefs on Creation, EC's hold to many different views on biological evolution. Variations in EC may include how much God was involved in the evolutionary process. Some believe that God created the first life on Earth, then allowed natural processes to work on all subsequent lifeforms. Others believe that God had a hand in the evolutionary process, guiding how evolution worked in the natural world.
When it comes to humans, again EC's hold to differing views. Some will say that Adam and Eve were historical figures, but that God chose them from the many Homo sapiens that had evolved from earlier primates. Others will suggest that Adam and Eve were not historical figures and that humans evolved from a large population of thousands of individuals, not just two (Adam and Eve).
Theologically, most EC's believe that Genesis One is not to be taken literally. They try and view it from an Ancient Near Eastern (ANE) perspective and accept a functional view of Genesis One, compared to the OEC view that it is an historical account of Creation. Two theologians, Drs. N. T. Wright and John H. Walton, provide the biblical understanding of the text to support this view. The largest organization that promotes Evolutionary Creationism is BioLogos.
EC's believe that the Flood of Noah was not an historical event. As with Genesis One and the Creation of the world, the purpose of the Flood story was to explain the sinfulness of man and God's removing this sin from the world. Since science does not show any evidence of a single, catastrophic worldwide flood event, most EC's believe that the Flood was based on a large Mesopotamian flood around 2900 B.C.