  The purpose of this tutorial paper is to present a broad overview of
photon-pair generation through the spontaneous four wave mixing (SFWM) process
in optical fibers. Progress in optical fiber technology means that today we
have at our disposal a wide variety of types of fiber, which together with the
fact that SFWM uses two pump fields, implies a truly remarkable versatility in
the resulting possible photon-pair properties. We discuss how the interplay of
the frequency, transverse mode, and polarization degrees of freedom, the first
linked to the latter two through fiber dispersion, leads to interesting
entanglement properties both in individual degrees of freedom and also
permitting hybrid and hyper entanglement in combinations of degrees of freedom.
This tutorial covers methods for photon pair factorability, frequency
tunability, and SFWM bandwidth control, the effect of frequency non-degenerate
and counter-propagating pumps, as well methods for characterizing photon pairs
generated in optical fibers.
