Abstract: This chapter provides a fairly detailed discussion of the renormalization group account of the universality of critical phenomena. This discussion allows one to determine the distinctive features of asymptotic explanation in general. Two other, superficially quite different, explanatory accounts involving “intermediate asymptotics” are then discussed. It is argued that these different examples exhibit the same general asymptotic explanatory strategy – one that is ubiquitous in physics and applied mathematics. The chapter concludes with a discussion of the importance of stability considerations in the asymptotic explanations.

Keywords: asymptotic explanation, critical phenomena, dimensional analysis, intermediate asymptotics, renormalization group, structural stability, universality,