The majority of recent peer-effect studies in education have focused on the effect of one particular type of peers on classmates. This view fails to take into account the reality that peer effects are heterogeneous for students with different characteristics, and that there are at least as many peer effect functions as there are types of peers. In this paper, we develop a general empirical framework that accounts for systematic interactions between peer types and nonlinearities of peer effects. We use machine-learning methods to (i) understand which dimensions of peer characteristics are the most predictive of academic success, (ii) estimate high-dimensional peer effects functions, and (iii) investigate performance-improving classroom allocation through policy-relevant simulations. First, we find that students’ own characteristics are the most predictive of academic success, and that the most predictive peer effects are generated by students with special needs, low-achieving students, and male students. Second, we show that peer effects traditionally reported by the literature likely miss important nonlinearities in the distribution of peer proportions. Third, we determine that classroom compositions that are the most balanced in students’ characteristics are the best ways to reach maximal aggregated school performance.