Large N flavor β-functions: A recap

β-Functions for abelian and nonabelian gauge theories are studied in the regime where the large N flavor expansion is applicable. The first nontrivial order in the 1/N expansion is known for any value of Nα, and there are also various indications as to the nature of higher order effects. The singularity structure as a function of Nα has implications for the existence of nontrivial fixed points.