In this paper we analyze the impact of classroom peers on individual student performance with a unique longitudinal data set covering all Florida public school students in grades 3-10 over a five-year period. Unlike many previous data sets used to study peer effects in education, our data set allow us to identify each member of a given student's classroom peer group in elementary, middle, and high school as well as the classroom teacher responsible for instruction. As a result, we can control for individual student fixed effects simultaneously with individual teacher fixed effects, thereby alleviating biases due to endogenous assignment of both peers and teachers, including some dynamic aspects of such assignments. Our estimation strategy, which focuses on the influence of peers' fixed characteristicsboth observed and unobservedon individual test score gains, also alleviates potential biases due to error in measuring peer quality, simultaneity of peer outcomes, and mean reversion. Under linear-inmeans specifications, estimated peer effects are small to non-existent, but we find some sizable and significant peer effects within non-linear models. For example, we find that peer effects depend on an individual student's own ability and on the ability level of the peers under consideration, results that suggest Pareto-improving redistributions of students across classrooms and/or schools. Estimated peer effects tend to be smaller when teacher fixed effects are included than when they are omitted, a result that suggests co-movement of peer and teacher quality effects within a student over time. We also find that peer effects tend to be stronger at the classroom level than at the grade level.