Photoacoustic imaging (PAI) is a rapidly developing hybrid biomedical imaging technology, which is capable of providing structural and functional information of biological tissues. Due to inevitable motion of the imaging object, such as respiration, heartbeat or eye rotation, motion artifacts are observed in the reconstructed images, which reduce the imaging resolution and increase the difficulty of obtaining high-quality images. This paper summarizes current methods for correcting and compensating motion artifacts in photoacoustic microscopy (PAM) and photoacoustic tomography (PAT), discusses their advantages and limits and forecasts possible future work.