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The distribution of gas-phase abundances in galaxy disks encodes the historyof nucleosynthesis and transport through the interstellar medium (ISM) overcosmic time. Multi-object and high resolution integral-field spectroscopy havestarted to measure these distributions across hundreds of HII regionsindividually resolved at $\lesssim 100$ pc scales in a handful of objects, butin the coming decade these studies will expand to larger samples of galaxies.This will allow us to understand the role of feedback and turbulence in drivingthe mixing and diffusion of metals in the ISM, and statistically assess therole of galaxy environment and disk dynamics in modifying how mixing proceeds.Detailed searches for over- and under-enriched regions can address to whatextent star formation is triggered by previous generations of star formationand by pristine and recycled gas flows. Local galaxies, for which thesedetailed measurements will be possible within the next decade, will inform theinterpretation of integrated measurements at high-z, where very differentdynamical gas-rich environments are found in early disk galaxies. Currently,progress in the field is severely hampered by the 0.2-0.3 dex level systematicuncertainties plaguing nebular abundance diagnostics. Improving our detailedunderstanding of ionized nebulae at $<$20 pc scales will help us find asolution to this problem, which will prove key to the study of metal enrichmentand mixing across the galaxy population in the next decade.

Mapping Gas Phase Abundances and Enrichment Patterns Across Galaxy Disks