Models of interspecific competition in a stochastic environment show that the effects of environmental fluctuations on species coexistence can be expected to vary from community to community. However, by taking account of some basic properties of the species in a community it is possible to predict whether environmental fluctuations should promote coexistence, promote competitive exclusion or have no effect on species coexistence. One such property is the way the growth rates of the species respond to the joint effects of environment and competition. In simple (additive) models the joint effect of environment and competition is the sum of their separate effects. Deviations from additivity, in either the direction of subadditivity or superadditivity, are important determinants of species coexistence in a fluctuating environment. Such nonadditive growth rates are predicted on the basis of life-history traits, heterogeneity within a population and heterogeneity in space. Nonadditive growth rates have intuitive interpretations in terms of buffers and amplifiers of the joint effects of environment and competition. A second property concerns the way fluctuations in the strength of competition are related to environmental fluctuations. We argue that favorable environmental conditions at some stage in the life cycle of an organism may lead to more competition for resources needed at a later stage, and hence positive covariance between environment and competition. In the presence of positive covariance, subadditive growth rates promote coexistence in a fluctuating environment, while superadditive growth rates promote competitive exclusion. Negative covariance between environment and competition reverses these conclusions.