Certainly, this is a topic with many levels of complexity, but in short, the idea of Darwinian evolution is not compatible with Scripture.
To be clear, the term evolution is loosely used today, but it should really be limited to the idea that creatures can transform into more complex creatures over time through small, gradual, genetic changes exclusively via natural processes. The word evolution should not be used solely to describe or refer to speciation or natural selection.
So why is evolution not compatible with Scripture?
Jesus, refering to Gen 1:27, stated: "But from the beginning of creation, 'God made them male and female.' (Mar 10:6 ESV). Notice that Jesus said, "at the beginning of creation" and not after millions of years. That alone dismisses any possibility of evolution being used by God to bring about the creatures we see today (aka Theistic Evolution).
The Bible allows for natural selection/speciation, or variation within a kind. Think of all the many different breeds of canines. The range of variation is great, yet they are all still fundamentally dogs. Natural selection/speciation is solid, scientific fact - it has been observed, tested and repeated.
The same cannot be said of Darwinian evolution, which insists that one kind of organsim will develop into another kind given enough time. Such a feat has never been observed in nature nor in the laboratory. As such, it cannot be tested nor confirmed. In fact, it should not be considered science at all; more accurately, evolution is more akin to a faith-based belief system. One that requires a tremendous amount of faith.
The book of Genesis tells us that humans and all earthly creatures were made by God, fully formed and functional, across two days (Gen 1:20-31). It also states that God made them according to their kinds.
Why is this important?
We don't typically use the term kind in our language today to describe types of animals. In modern terminology, the taxonomic hierarchy of Family, is in many cases, closest to the Biblical kind. For example, the Family Canidae includes all dogs, wolves, foxes, etc. In simplest terms, dogs will always give birth to other dogs and dog types, never to something that is not a dog, much less a cat. Neither can one breed a cat with a dog because they are of different kinds. But you can breed a tiger and a lion, resulting in a liger - because they belong to the same cat kind.
Taking another look at these verses shows that at the end of creation, God called His work "very good." If evolution is true, then how could God call the supposed millions of years of death, disease, and predation "very good?" In addition to that, Paul wrote that death entered the world through sin (Rom 5:12), the sin from Adam. The Bible teaches that death came after man arrived, again in contradiction to evolution.
There are many other arguments that could be made on this topic. Ultimately, one must decide to believe the infallible, unchanging Word of God or man's fallible, frequently changing ideas.
Even though millions of samples have been found, the fossil record has failed to provide evidence of any transitional forms to support Darwinian evolution. Yet, according to Darwin himself in his book Origin of the Species, the geologic strata should be filled with intermediate, or transitional, links of one animal transforming into another.
Because of the lack of transitional fossils, evolutionary biologists point out anatomically similar features in different animals, claiming that these similarities indicate common ancestry. These similarities do not prove a common ancestor, but rather a Common Designer that used similar structures across different animal kinds.