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A key characteristic of heterodox theories of the business cycle is their focus on endogenous business cycle mechanisms. This paper provides an overview and comparison of four models in heterodox business cycle theory: multiplier-accelerator models, Goodwin models, Minskyan debt-cycle models, and momentum trader models. A representative model from each theory is formulated as a two-dimensional predator-prey system in continuous time, which allows us to identify the different stabilizing and destabilizing mechanisms. We argue that the theories are substantially competing, as they posit different mechanisms that explain cycles, but we also argue that these mechanisms are not mutually exclusive. We suggest that heterodox economists work toward a synthesis.