  The Sagnac effect can be described as the difference in travel time between
two photons traveling along the same path in opposite directions. In this paper
we explore the consequences of this characterisation in the context of General
Relativity. We derive a general expression for this time difference in an
arbitrary space-time for arbitrary paths. In general, this formula is not very
useful since it involves solving a differential equation along the path.
However, we also present special cases where a closed form expression for the
time difference can be given. The main part of the paper deals with the
discussion of the effect in a small neighbourhood of an arbitrarily moving
observer in their arbitrarily rotating reference frame. We also discuss the
special case of stationary space-times and point out the relationship between
the Sagnac effect and Fizeau's "aether-drag" experiment.
