Charles Darwin is well known as having popularized the concept of natural selection. Despite widespread teaching of the topic in biology related contexts, it is actually controversial among scientists. This is true in both evolutionary and creationary circles. To assess the role natural selection plays in our world, it must first be defined in a scientifically rigorous manner. Mathematical tools can help in assessing its role; comparison with principles known from artificial selection can be informative as well. With various methods of mathematical modeling and statistical tests, there are important assumptions that should be recognized to avoid premature conclusions about the results. Finally, field observation provides important data that needs to be considered. Examination of each of these areas leads to several conclusions. Natural selection has not played a significant positive role in the history of life on earth for sexually reproducing animals such as mammals and birds. Statistical tests, which are a valid means to screen for natural selection and comprise the one line of evidence that often seems to support its occurrence in adaptation, have not been validated; many of the non-random patterns detected probably have little to do with the action of natural selection. Naturalistic assumptions, which include assuming meiotic drive (which distorts Mendelian inheritance) is a random mechanism, appear to have hindered for decades our understanding of how creatures adapt. A reasonable creationary prediction is that mechanisms such as biased gene conversion (one form of meiotic drive) will turn out to be designed to alter the frequency of alleles in a way that aids in adaptation of the population.