  After a brief introduction to the Heavy-Quark Effective Theory (HQET), I
review the extraction of the Isgur-Wise function from lattice QCD calculations
of the matrix elements for semi-leptonic decays of heavy-light pseudoscalar
mesons both into pseudoscalar and into vector mesons. This work is beginning to
test the heavy-quark spin-flavour symmetries around the charm mass and to
indicate the size of $O(1/m_c)$ corrections. An alternative approach to put the
HQET on the lattice offers the prospect of computing the Isgur-Wise function
directly.
