Interpretation of the photoluminescence (PL) decay kinetics in metal halide perovskites (MHPs) is extremely important for understanding the mechanisms and control of charge recombination in these promising photovoltaic and optoelectronic materials. In this work, we give a review of current models describing the PL decay kinetics in MHP layers and nanocrystals with particular attention to the interpretation of long-lived PL decay components (hundreds of nanoseconds to microseconds). First, we analyze phenomenological photophysical models based on the rate equations, which describe the charge carrier recombination in MHP layers as an exclusively intrinsic bulk process. An important role of the carrier diffusion and nonradiative recombination on the layer surfaces is then discussed. A recently published approach is then analyzed, in the framework of which the observed long-lived components of PL decay kinetics in MHP nanocrystals are described in terms of the delayed luminescence mechanism arising due to the processes of multiple trapping and detrapping of carriers by shallow nonquenching traps. The possible origin of the shallow traps and perspectives to include the carrier trapping and detrapping processes in a model describing PL kinetics in MHP layers are discussed.