Competition between herbivorous insects often occurs as a trait mediated indirect effect mediated by inducible changes in plant quality rather than a direct effect mediated by plant biomass. While plant-mediated competition likely influences many herbivores, progress linking studies of plant-mediated competition in terrestrial phytophagous insects to longer-term consequences for herbivore communities has been elusive, and there is little relevant theory to guide this effort. We present simple models describing plant-mediated interactions between two herbivorous insects or other functionally equivalent organisms. These models consider general features of plant-mediated competition including specificity of elicitation by and effects on herbivores, positive and negative interactions among herbivores, competition independent of changes in plant biomass, and the existence of multiple relevant plant traits. Our analyses generate four important conclusions. First, herbivores competing strongly via only one plant quality phenotype exhibit a limited range of outcomes. These include coexistence and competitive exclusion of either herbivore, but do not include initial condition dependence. Second, when the outcome of competition is competitive exclusion, the herbivore that persists is the one that can do so under the highest inducible reductions in plant quality. Third, competition via more than one inducible phenotype can exhibit a wider range of outcomes including multiple equilibria and initial condition dependence. Finally, transient dynamics may not predict the eventual outcome of competition when changes in plant quality are slow relative to herbivore population growth, especially when herbivores compete through multiple phenotypes. We interpret our results in terms of competition outcomes reported in the literature, and suggest directions for the future empirical study of herbivore competition mediated by inducible changes in plant quality.