Flow imaging is an important method for quantification in many medical imaging modalities, with applications ranging from estimating wall shear rate to detecting angiogenesis. Modalities like ultrasound and optical coherence tomography both offer flow imaging capabilities, but suffer from low contrast to red blood cells and are sensitive to clutter artefacts. Photoacoustic imaging (PAI) is a relatively new field, with a recent interest in flow imaging. The recent enthusiasm for PA flow imaging is due to its intrinsic contrast to haemoglobin, which offers a new spin on existing methods of flow imaging, and some unique approaches in addition. This review article will delve into the research on photoacoustic flow imaging, explain the principles behind the many techniques and comment on their individual advantages and disadvantages.