A new chapter in the long and distinguished history of perovskites is being written with the breakthrough success of metal halide perovskites (MHPs) as solution-processed photovoltaic (PV) absorbers. The current surge in MHP research has largely arisen out of their rapid progress in PV devices; however, these materials are potentially suitable for a diverse array of optoelectronic applications. Like oxide perovskites, MHPs have ABX stoichiometry, where A and B are cations and X is a halide anion. Here, the underlying physical and photophysical properties of inorganic (A = inorganic) and hybrid organic-inorganic (A = organic) MHPs are reviewed with an eye toward their potential application in emerging optoelectronic technologies. Significant attention is given to the prototypical compound methylammonium lead iodide (CHNHPbI) due to the preponderance of experimental and theoretical studies surrounding this material. We also discuss other salient MHP systems, including 2-dimensional compounds, where relevant. More specifically, this review is a critical account of the interrelation between MHP electronic structure, absorption, emission, carrier dynamics and transport, and other relevant photophysical processes that have propelled these materials to the forefront of modern optoelectronics research.