Stellar populations contain the most important information about star cluster formation and evolution. Until several decades ago, star clusters were believed to be ideal laboratories for studies of simple stellar populations (SSPs). However, discoveries of multiple stellar populations in Galactic globular clusters have expanded our view on stellar populations in star clusters. They have simultaneously generated a number of controversies, particularly as to whether young star clusters may have the same origin as old globular clusters. In addition, extensive studies have revealed that the SSP scenario does not seem to hold for some intermediate-age and young star clusters either, thus making the origin of multiple stellar populations in star clusters even more complicated. Stellar population anomalies in numerous star clusters are well-documented, implying that the notion of star clusters as true SSPs faces serious challenges. In this review, we focus on stellar populations in massive clusters with different ages. We present the history and progress of research in this active field, as well as some of the most recent improvements, including observational results and scenarios that have been proposed to explain the observations. Although our current ability to determine the origin of multiple stellar populations in star clusters is unsatisfactory, we propose a number of promising projects that may contribute to a significantly improved understanding of this subject.