  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.
