  The abundant production of beauty and charm hadrons in the $5 \times 10^{12}$
$Z^0$ decays expected at FCC-ee offers outstanding opportunities in flavour
physics that in general exceed those available at Belle II, and are
complementary to the heavy-flavour programme of the LHC. A wide range of
measurements will be possible in heavy-flavour spectroscopy, rare decays of
heavy-flavoured particles and $C\!P$-violation studies, which will benefit from
the low-background experimental environment, the high Lorentz boost, and the
availability of the full spectrum of hadron species. This essay first surveys
the important questions in heavy-flavour physics, and assesses the likely
theoretical and experimental landscape at the turn-on of FCC-ee. From this
certain measurements are identified where the impact of FCC-ee will be
particularly important. A full exploitation of the heavy-flavour potential of
FCC-ee places specific constraints and challenges on detector design, which in
some cases are in tension with those imposed by the other physics goals of the
facility. These requirements and conflicts are discussed.
