Darwin's theory of natural selection lacked an adequate account of inheritance, making it logically incomplete. We review the interaction between evolution and genetics, showing how, unlike Mendel, Darwin's lack of a model of the mechanism of inheritance left him unable to interpret his own data that showed Mendelian ratios, even though he shared with Mendel a more mathematical and probabilistic outlook than most biologists of his time. Darwin's own "pangenesis" model provided a mechanism for generating ample variability on which selection could act. It involved, however, the inheritance of characters acquired during an organism's life, which Darwin himself knew could not explain some evolutionary situations. Once the particulate basis of genetics was understood, it was seen to allow variation to be passed intact to new generations, and evolution could then be understood as a process of changes in the frequencies of stable variants. Evolutionary genetics subsequently developed as a central part of biology. Darwinian principles now play a greater role in biology than ever before, which we illustrate with some examples of studies of natural selection that use DNA sequence data and with some recent advances in answering questions first asked by Darwin.