The problem of simplicity involves three questions: How is the simplicity of a hypothesis to be measured? How is the use of simplicity as a guide to hypothesis choice to be justified? And how is simplicity related to other desirable features of hypotheses -- that is, how is simplicity to be traded-off? The present paper explores these three questions, from a variety of viewpoints, including Bayesianism, likelihoodism, and the framework of predictive accuracy formulated by Akaike (1973). It may turn out that simplicity has no global justification -- that its justification varies from problem to problem.