This paper explores the role and limits of cognitive simulation in understanding or explaining others. In simulation, one puts one’s own cognitive processes to work on pretend input similar to that one supposes that the other plausibly had. Such a process is highly useful. However, it is also limited in important ways. Several limitations fall out from the various forms of cognitive diversity. Some of this diversity results from cultural differences, or from differences in individuals’ cognitive biographies. Such diversity is clearly important in history. Some sorts of such diversity are discussed, with attention to the results of contemporary cognitive science. It is argued that one must sometimes employ mixed (simulation-based/theory-based) strategies, and that sometimes what is done will be neither purely simulation nor purely theory-based.