Aspects of heavy-quark theory

Recent achievements in heavy-quark theory are critically reviewed. The emphasis is put on those aspects that either did not attract enough attention or cause heated debates in the current literature. Among other topics we discuss (a) basic parameters of the heavy-quark theory; (b) a class of exact QCD inequalities; (c) new heavy quark sum rules; (d) the virial theorem; (e) applications (|V_cb| from the total semileptonic width and from the B → D* transition at zero recoil). In some instances new derivations of previously known results are given, or new aspects addressed. In particular, we dwell on the exact QCD inequalities. Furthermore, a toy model is considered that may shed light on the controversy regarding the value of the kinetic energy of heavy quarks obtained by different methods.