  Stokes' theorem is central to many aspects of physics -- electromagnetism,
the Aharonov-Bohm effect, and Wilson loops to name a few. However, the
pedagogical examples and research work almost exclusively focus on situations
where the fields are time-independent so that one need only deal with purely
spatial line integrals ({\it e.g.} $\oint {\bf A} \cdot d{\bf x}$) and purely
spatial area integrals ({\it e.g.} $\int (\nabla \times {\bf A}) \cdot d{\bf a}
= \int {\bf B} \cdot d{\bf a}$). Here we address this gap by giving some
explicit examples of how Stokes' theorem plays out with time-dependent fields
in a full 4-dimensional spacetime context. We also discuss some unusual
features of Stokes' theorem with time-dependent fields related to gauge
transformations and non-simply connected topology.
