  In this article we review recent progress in the understanding of multiband
superconductivity and its relationship to odd-frequency pairing. We begin our
discussion by reviewing the emergence of odd-frequency pairing in a simple
two-band model, providing a brief pedagogical overview of the formalism. We
then examine several examples of multiband superconducting systems in each case
describing, both, the origin of the band degree of freedom and the nature of
the odd-frequency pairing. Throughout, we attempt to convey a unified picture
of how odd-frequency pairing emerges in these materials and propose that
similar mechanisms are responsible for odd-frequency pairing in several
analogous systems: layered two-dimensional heterostructures, double quantum
dots, double nanowires, Josephson junctions, and systems described by isolated
valleys in momentum space. We also review experimental probes of odd-frequency
pairing in multiband systems, focusing on hybridization gaps in the electronic
density of states, paramagnetic Meissner effect, and Kerr effect.
