High-performance perovskite solar cells (PSCs) based on organometal halide perovskite have emerged in the past five years as excellent devices for harvesting solar energy. Some remaining challenges should be resolved to continue the momentum in their development. The photocurrent density-voltage (J-V) responses of the PSCs demonstrate anomalous dependence on the voltage scan direction/rate/range, voltage conditioning history, and device configuration. The hysteretic J-V behavior presents a challenge for determining the accurate power conversion efficiency of the PSCs. Here, we review the recent progress on the investigation of the origin(s) of J-V hysteresis behavior in PSCs. We discuss the impact of slow transient capacitive current, trapping and detrapping process, ion migrations, and ferroelectric polarization on the hysteresis behavior. The remaining issues and future research required toward the understanding of J-V hysteresis in PSCs will also be discussed.