The basic forward model in Population Genetics is called the Wright-Fisher model, which is a Markov chain describing the evolution of the distribution of types in a finite, fixed size population. There is a limiting model as the population size goes to infinity called the Kimura diffusion model, which takes place on a simplex. I will discuss some recent analytic work on this class of equations and the subtleties that arise in their numerical solution. The focus will be on the 1-dimensional case, which is already very complicated.