What is the current theory of evolution?

That is a very hard question to answer as the "Theory of Evolution" is really an umbrella term for several theories based on the fact that allele frequencies of populations change over time, and the assumption that they have done so for the entirety of life on earth, as well as continuing on into the future.

Evolution does NOT claim that there is no God. It makes NO STATEMENT whatsoever about spiritual matters. In fact, statistically speaking, the majority of the people who accept evolution are christians. It also does NOT include big-bang cosmology, does not require a multi-billion year-old earth, and does NOT address the origin of life at all, only its' variety.

Current evolutionary theory can be traced to the moment when Darwin proposed his theory on the mechanics of evolution which overturned the previously held view proposed by LaMarck.

LaMarcks theory of evolution proposed that an animal gains a trait in its' lifetime and then passes it on.

Darwins theory replaced LaMarcks theory by proposing that changes were inherited, but not acquired during the lifetime of the individual. He attributed these changes to random mutations present from birth.

Darwin did not stop with a mechanism for these changes, he also divised the "theory of Natural Selection" as a mechanism to favor beneficial mutations.

Later, he proposed his "theory of Common Descent" as an explanation of the current variety we see in life. This theory proposes that at some point in the distant past, all living things share a common ancestor.

Darwins three ideas have been confirmed through genetics, phylogenics, taxonomy, and Paleontology, as well as being supported by every branch of science which can address Biology.

Through more discoveries, other scientists have developed even more specific theories based on evolution such as, "punctuated equilibrium", "evo-devo", and even the "Out of Africa" theory of human origins.

The more we understand about the history of life, the more theories will be developed, but they are all part of evolutionary theory.