This chapter reviews how galactic inflows influence galaxy metallicity. The goal is to discuss predictions from theoretical models, but particular emphasis is placed on the insights that result from using models to interpret observations. Even as the classical "G-dwarf problem" endures in the latest round of observational confirmation, a rich and tantalizing new phenomenology of relationships between M * , Z, SFR, and gas fraction is emerging both in observations and in theoretical models. A consensus interpretation is emerging in which star-forming galaxies do most of their growing in a quiescent way that balances gas inflows and gas processing, and metal dilution with enrichment. Models that explicitly invoke this idea via equilibrium conditions can be used to infer inflow rates from observations, while models that do not assume equilibrium growth tend to recover it self-consistently. Mergers are an overall subdominant mechanism for delivering fresh gas to galaxies, but they trigger radial flows of previously-accreted gas that flatten radial gas-phase metallicity gradients and temporarily suppress central metallicities. Radial gradients are generically expected to be steep at early times and then flattened by mergers and enriched inflows of recycled gas at late times. However, further theoretical work is required in order to understand how to interpret observations. Likewise, more observational work is needed in order to understand how metallicity gradients evolve to high redshifts.