Hybrid organic-inorganic metal halide perovskites have recently emerged as exciting new light-harvesting and charge-transporting materials for efficient photovoltaic devices. Yet knowledge of the nature of the photogenerated excitations and their subsequent dynamics is only just emerging. This article reviews the current state of the field, focusing first on a description of the crystal and electronic band structure that give rise to the strong optical transitions that enable light harvesting. An overview is presented of the numerous experimental approaches toward determining values for exciton binding energies, which appear to be small (a few milli-electron volts to a few tens of milli-electron volts) and depend significantly on temperature because of associated changes in the dielectric function. Experimental evidence for charge-carrier relaxation dynamics within the first few picoseconds after excitation is discussed in terms of thermalization, cooling, and many-body effects. Charge-carrier recombination mechanisms are reviewed, encompassing trap-assisted nonradiative recombination that is highly specific to processing conditions, radiative bimolecular (electron-hole) recombination, and nonradiative many-body (Auger) mechanisms.