Arterial spin labeling (ASL) perfusion MRI is a non-invasive technique for quantifying and mapping cerebral blood flow (CBF). Depending on the tissue signal change after magnetically labeled arterial blood enters the brain tissue, ASL MRI signal can be affected by several factors, including the volume of arrived arterial blood, signal decay of labeled blood, physiological fluctuations of the brain and CBF, and head motion, etc. Some of them can be controlled using sophisticated state-of-art ASL MRI sequences, but the others can only be resolved with post-processing strategies. Over the decades, various post-processing methods have been proposed in the literature, and many post processing software packages have been released. This self-contained review provides a brief introduction to ASL MRI, recommendations for typical ASL MRI data acquisition protocols, an overview of the ASL data processing pipeline, and an introduction to typical methods used at each step in the pipeline. Although the main focus is on traditional heuristic model-based methods, a brief introduction to recent machine learning-based approaches is provided too.