  We discuss the chemical evolution of dwarf irregular and blue compact
galaxies in light of recent data, new stellar yields and chemical evolution
models. We examine the abundance data for evidence of HII region
self-enrichment effects, which would lead to correlations in the scatter of
helium, nitrogen, and oxygen abundances around their mean trends. The observed
helium abundance trends show no such correlations, though the nitrogen--oxygen
trend does show strong evidence for real scatter beyond observational error. We
construct simple models for the chemical evolution of these galaxies, using the
most recent yields of \he4, C, N and O in intermediate- and high-mass stars.
The effects of galactic outflows, which can arise both from bulk heating and
evaporation of the ISM, and from the partial escape of enriched supernova
ejecta are included. In agreement with other studies, we find that
supernova-enriched outflows can roughly reproduce the observed He, C, N, and O
trends; however, in models that fit N versus O, the slopes $\Delta Y/\Delta$O
and $\Delta Y/\Delta$N consistently fall more than $2\sigma$ below the fit to
observations. We discuss the role of the models and their uncertainties in the
extrapolation of primordial helium from the data. We also explore the model
dependence arising nucleosynthesis uncertainties associated with nitrogen
yields in intermediate mass stars, the fate of $8-11 \msol$ stars, and massive
star winds.
