I have been reading and following the evolution debate for many, many years. A great deal of conflict comes from different people using the same terms to mean different things.
The word “evolution” or even the “theory of evolution” is often used by different people differently. Natural selection, meaning that organisms that reproduce better will have their offspring eventually take over a given population is just simple logic. That mutations occur on a regular basis has been demonstrated. If all people mean by evolution is the above then it has been pretty much proven.
What has not been demonstrated (what PBO means) is that a series of small mutations together with natural selection can succeed in changing a hippo-like creature into a whale or a monkey-like creature into a man or a fish-like creature into a lizard.
Evidence for this latter claim (often called macro-evolution) is circumstantial (i.e. things like vestigial organs) but it has never been demonstrated experimentally.
Poppa is also right that biology is not “based on” evolution in any practical sense. One can be a fantastic biologist or medical doctor without subscribing to macro-evolutionary theory. When biologists say that their field is based on evolution, they mean that they use evolution based terminology to discuss things and that it is taken as a given.
Another concept many people mean when they use the word “evolution” is the common descent of all life from a single organism or a small number of simple organisms. The Neo-Darwinian theory of evolution is an attempt to explain how common descent happened.