Abstract: Limits on the charged lepton flavor violating (CLFV) process of μ→e conversion are expected to improve by four orders of magnitude due to the next generation of experiments, Mu2e at Fermilab and COMET at J-PARC. The kinematics of the decay of a trapped muon are ideal for detecting a signal of CLFV, but the intervening nuclear physics presents a significant roadblock to the interpretation of experimental results. We introduce an effective theory of μ→e conversion formulated at the nuclear scale, which factorizes the nuclear physics from the CLFV leptonic physics, sequestering the latter quantity into unknown low-energy constants (LECs) that are probed directly by experiments. Utilizing state-of-the-art shell-model calculations of nuclear response functions, we discuss how a program of μ→e conversion measurements on different targets—selected for their nuclear ground-state properties—could constrain the unknown LECs. Finally, we discuss the relationship of the nuclear effective theory to higher-energy effective theories.