  I give an introduction to the theory of preasymptotic effects based on the
systematic OPE/HQET expansion in $1/m_Q$ where $m_Q$ is the heavy quark mass.
The general idea is explained in two most instructive examples, with an
emphasis on pedagogical aspects. Some important results of the last year are
reviewed. In discussing the issue of the quark-hadron duality, one of the basic
ingredients of the theory, I prove that the operator product expansion {\em per
se} is an asymptotic expansion. The behavior of the high order terms in this
expansion determines the onset of duality and the accuracy of the duality
relations. The factorial divergence of the high-order terms in OPE implies a
sophisticated analytical structure in the $\alpha_s$ plane, with terms of the
type $\exp [-\exp (1/\alpha_s )]$.
