The happy-productive worker thesis (HPWT) assumes that happy employees perform better. Given the relevance of teams and work-units in organizations, our aim is to analyze the state of the art on happy-productive work-units (HPWU) through a systematic review and integrate existing research on different collective well-being constructs and collective performance. Research on HPWU (30 studies, 2001-2018) has developed through different constructs of well-being (hedonic: team satisfaction, group affect; and eudaimonic: team engagement) and diverse operationalizations of performance (self-rated team performance, leader-rated team performance, customers' satisfaction, and objective indicators), thus creating a disintegrated body of knowledge about HPWU. The theoretical frameworks to explain the HPWU relationship are attitude-behavior models, broaden-and-build theory, and the job-demands-resources model. Research models include a variety of antecedents, mediators, and moderating third variables. Most studies are cross-sectional, all propose a causal happy-productive relationship (not the reverse), and generally find positive significant relationships. Scarce but interesting time-lagged evidence supports a causal chain in which collective well-being leads to team performance (organizational citizenship behavior or team creativity), which then leads to objective work-unit performance. To conclude, we identify common issues and challenges across the studies on HPWU, and set out an agenda for future research.