This paper describes recent work on computational methods for the coalescent. We show how integro-recurrence relations for sampling distributions and related quantities may be solved by a simple Markov chain Monte Carlo method. We describe the method in the context of the coalescent process for a population that is evolving according to a deterministic population size function. The usual constant population size models appear as a special case of this approach. One of the appealing features of the approach is its generic nature: many apparently different problems may be attacked with this one approach. A wide variety of examples are discussed, among them maximum likelihood estimation of parameters.