The past 20 years has seen a remarkable growth in the use of statistics as evidence in legal proceedings. In the United States especially, there has been a vigorous debate over the role Bayesian methods should have both in the presentation of such evidence and in its evaluation by the triers of fact, i.e., judges and juries. In this paper, we review some of the legal and statistical elements of this debate, especially as it has appeared in treatises on legal evidence and we consider empirical evidence on how Bayesian evidence would be understood by triers of fact. We then present some widely discussed issues and "problematic" aspects of some simple uses of Bayes' theorem. Finally, we describe two recent court cases involving Bayesian statistical evidence.