Recent progress in the understanding of multiband superconductivity and its relationship to odd-frequency pairing are reviewed herein. The discussion begins by reviewing the emergence of odd-frequency pairing in a simple two-band model, providing a brief pedagogical overview of the formalism. Several examples of multiband superconducting systems are examined, in each case describing both the origin of the band degree of freedom and the nature of the odd-frequency pairing. Throughout, it is attempted 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 2D heterostructures, double quantum dots, double nanowires, Josephson junctions, and systems described by isolated valleys in momentum space. In addition, experimental probes of odd-frequency pairing in multiband systems are reviewed, focusing on hybridization gaps in the electronic density of states, paramagnetic Meissner effect, and Kerr effect.