The formation of long-term pair bonds in marine fish has elicited much empirical study. However, the evolutionary mechanisms involved remain contested and previous theoretical frameworks developed to explain monogamy in birds and mammals are not applicable to many cases of monogamy in marine fish. In this review, we summarise all reported occurrences of social monogamy in marine fish, which has so far been observed in 18 fish families. We test quantitatively the role of ecological and behavioural traits previously suggested to be important for the evolution of monogamy and show that monogamous species occur primarily in the tropics and are associated with coral reef environments in which territory defence and site attachment is facilitated. However, there is little evidence that obligately monogamous species are smaller in body size than species that can adopt a polygynous mating system. We review the evidence pertaining to six hypotheses suggested for the evolution of monogamous pair bonds: (1) biparental care, (2) habitat limitation, (3) low population density/low mate availability/low mobility, (4) increased reproductive efficiency, (5) territory defence, and (6) net benefit of single mate sequestration. We outline predictions and associated empirical tests that can distinguish between these hypotheses, and assess how generally each hypothesis explains monogamy within and between breeding periods for species with different types of territories (i.e. feeding only or feeding and breeding). Hypotheses (1) and (2) have limited applicability to marine fishes, while hypotheses (3)–(5) have little empirical support beyond the species for which they were designed. However, the role of paternal care in promoting monogamous pair bonds is not explicit in these hypotheses, yet paternal care has been reported in more than 70 monogamous marine fish. We show that paternal care may act to increase the likelihood of monogamy in combination with each of the proposed hypotheses through decreased benefits to males from searching for additional mates or increased advantages to females from sequestering a single high-quality mate. Among species defending breeding and feeding territories, the benefits, both within and between reproductive periods, of sequestering a single high-quality mate (hypothesis 6) appear to be the best explanation for socially monogamous pairs. For species without parental care (i.e. holding only feeding territories), territory defence (hypothesis 5) in combination with the benefits of guarding a large mate (hypothesis 6) could potentially explain most instances of monogamy. Empirical studies of marine fishes over the past two decades are therefore slowly changing the view of monogamy from a mating system imposed upon species by environmental constraints to one with direct benefits to both sexes.