A state-of-the-art review on the Probable Maximum Precipitation (PMP) as it relates to climate variability and change is presented. The review consists of an examination of the current practice and the various developments published in literature. The focus is on relevant research where the effect of climate dynamics on the PMP are discussed as well as statistical methods developed for estimating very large extreme precipitation including the PMP. Often confusion arises on the interpretation of extreme events without considering the effect of low frequency components of the climate system, their probabilistic nature that may be described by heavy-tail models, and the effect of the uncertainty of several factors determining them, such as atmospheric moisture, its transport into storms, wind, and their future changes. The review examines these issues as well as the underlying historical and proxy data. In addition, we summarize the procedures and guidelines established by some countries (e.g. USA, Australia, Canada, UK, EU, and others), states (e.g. California, Quebec), and the current manual of the World Meteorological Organization for estimating the PMP. In doing so, we paid attention whether the current guidelines and research published literature take into consideration the effects of the variability and change of climatic processes and the underlying uncertainties.