Predictive Process Monitoring (PPM) extends classical process mining techniques by providing predictive models that can be applied at runtime during the execution of a business process, for example, to predict the sequence of the next event(s) in a case, its outcomes, or performance-related aspects such as the remaining processing time. These predictive models go beyond process mining’s inherent descriptive nature that is offered by typical process discovery, conformance checking, and model enhancement techniques. The growing interest in PPM is driven by its additional value proposition, i.e., delivering real-time information regarding the future execution of business process instances, thus allowing for better informed operational decision making and performance analysis. The rapid growth of PPM during the last ten years has left the field lacking a cohesive taxonomy and an explicit recognition of the prevailing challenges. This paper aims at closing this gap, by comprehensively defining PPM using a unified approach to the key terms and by discussing challenges and opportunities in the field. Specifically, we propose three overarching research challenges and nine research directions, which have been validated through a survey with PPM researchers.