The Problem of Quark and Lepton Masses

Different approaches to the fermion mass problem are reviewed. We illustrate these approaches by summarizing recent developments in models of quark and lepton mass matrices. Dynamical calculations of the top quark mass are discussed, based on (a) infrared quasi-fixed points of the renormalisation group equations, and (b) the multiple point criticality principle in the pure Standard Model. We also consider Yukawa unification and mass matrix texture. Models with approximately conserved gauged chiral flavour charges beyond the Standard Model are shown to naturally give a fermion mass hierarchy.