Large language models (LLMs), through their exposure to massive collections of online text, learn to reproduce the perspectives and linguistic styles of diverse social and cultural groups. This capability suggests a powerful social scientific application--the simulation of empirically realistic, culturally situated human subjects. Synthesizing recent research in artificial intelligence and computational social science, we outline a methodological foundation for simulating human subjects and their social interactions. We then identify six characteristics of current models that are likely to impair the realistic simulation of human subjects: bias, uniformity, atemporality, disembodiment, linguistic cultures, and alien intelligence. For each of these areas, we discuss promising approaches for overcoming their associated shortcomings. Given the rate of change of these models, we advocate for an ongoing methodological program for the simulation of human subjects that keeps pace with rapid technical progress, and caution that validation against human subjects data remains essential to ensure simulation accuracy.