The planetary population synthesis method aims at comprehensively testing planet formation theories against observational evidence and providing theoretical sets of planets to help interpret observations and inform instrument development. Recent developments on the theoretical and observational sides are reviewed: First, observational constraints are summarized, and then, the workflow of population synthesis and its two main components are presented, which are global end-to-end models of planetary formation and evolution and probability distributions for the disk initial conditions. Next, the output of four recent population synthesis models is compared in detail, and differences and similarities are discussed. The goal is to help the reader understand the assumptions that were made and how they impact the results. Furthermore, future directions of research are identified, and the impact of current and future observational programs is discussed. With JWST, evidence on disk and planet compositions emerges. Planet formation models need to prepare for these near-future developments by including self-consistent magnetic wind-driven gas and dust disk evolution, and planetary migration as well as employ hybrid pebble and planetesimal accretion, which are identified as dominant modes of accretion in different mass regimes.