Organic-inorganic lead halide perovskites are distinct from most other semiconductors because they exhibit characteristics of both electronic and ionic motion. Accurate understanding of the optoelectronic impact of such properties is important to fully optimize devices and be aware of any limitations of perovskite solar cells and broader optoelectronic devices. Here we use a numerical drift-diffusion model to describe device operation of perovskite solar cells. To achieve hysteresis in the modeled current-voltage characteristics, we must include both ion migration and electronic charge traps, serving as recombination centers. Trapped electronic charges recombine with oppositely charged free electronic carriers, of which the density depends on the bias-dependent ion distribution in the perovskite. Our results therefore show that reduction of either the density of mobile ionic species or carrier trapping at the perovskite interface will remove the adverse hysteresis in perovskite solar cells. This gives a clear target for ongoing research effort and unifies previously conflicting experimental observations and theories.