Absorbing phase transitions are a category of non-equilibrium phase transition that have been studied extensively in classical systems. More recently, there has been interest in the study of such phenomena also in quantum systems. In this regard, key questions remain as to the possible universality classes and the relevance of any quantum effects in determining such classes. In this talk, I will introduce some of the basic ideas of absorbing phase transitions, along with an overview of some results from the past two years for quantum systems in both continuous and discrete time models.