Why do so many species coexist despite the competitive exclusion principle? This question is at the core of extensive community ecology research. Peter Chesson's coexistence theory provides an important framework for synthesizing the various mechanisms that promote species coexistence. In this framework, the balance between stabilizing effects, i.e., mechanisms promoting negative frequency-dependence, and equalizing effects, i.e., mechanisms reducing differences in competitive ability, determines competition outcomes. By decomposing invasion growth rates, the framework allows for quantification of the importance of processes in stable environments, such as resource partitioning and species-specific enemies, relative to that of processes in temporally and spatially fluctuating environments, such as the storage effect and relative nonlinearity. Despite its mathematical complexity, it can guide empirical studies and provide a significant step toward synthesizing various coexistence mechanisms in community ecology theory. We provide an illustrated guide to this theoretical framework and discuss future perspectives on community ecology research on species coexistence.