  The key quantity of the heavy quark theory is the quark mass $m_Q$. Since
quarks are unobservable one can suggest different definitions of $m_Q$. One of
the most popular choices is the pole quark mass routinely used in perturbative
calculations and in some analyses based on heavy quark expansions. We show that
no precise definition of the pole mass can be given in the full theory once
non-perturbative effects are included. Any definition of this quantity suffers
from an intrinsic uncertainty of order $\Lam /m_Q$. This fact is succinctly
described by the existence of an infrared renormalon generating a factorial
divergence in the high-order coefficients of the $\alpha_s$ series; the
corresponding singularity in the Borel plane is situated at $2\pi /b$. A
peculiar feature is that this renormalon is not associated with the matrix
element of a local operator. The difference $\La \equiv M_{H_Q}-m_Q^{pole}$ can
still be defined in Heavy Quark Effective Theory, but only at the price of
introducing an explicit dependence on a normalization point $\mu$: $\La (\mu
)$. Fortunately the pole mass $m_Q(0)$ {\em per se} does not appear in
calculable observable quantities.
