Ecologists working on population cycles of arvicoline (microtine) rodents consider three ecological mechanisms as the most likely explanations of this long-standing puzzle in population ecology: maternal effects, interaction with specialist predators, and interaction with the food supply. Each of these hypotheses has now been translated into parameterized models, and has been shown to be capable of generating second-order oscillations (that is, population cycles driven by delayed density dependence). This development places us in a unique situation for population ecology. We can now practice “strong inference” by explicitly and quantitatively comparing the predictions of the three rival hypotheses with data. In this review, we contrast the ability of each hypothesis to explain various empirically observed features of rodent cycles, with a particular emphasis on the well-studied case of Microtus agrestis and other small rodents in Fennoscandia (Finland, Sweden and Norway). Our conclusion is that the current evidence best supports the predation hypothesis.