  Operator product expansions (OPEs) in quantum field theory (QFT) provide an
asymptotic relation between products of local fields defined at points $x_1,
\dots, x_n$ and local fields at point $y$ in the limit $x_1, \dots, x_n \to y$.
They thereby capture in a precise way the singular behavior of products of
quantum fields at a point as well as their ``finite trends.'' In this article,
we shall review the fundamental properties of OPEs and their role in the
formulation of interacting QFT in curved spacetime, the ``flow relations'' in
coupling parameters satisfied by the OPE coefficients, the role of OPEs in
conformal field theories, and the manner in which general theorems --
specifically, the PCT theorem -- can be formulated using OPEs in a curved
spacetime setting.
