The antibody repertoire of each individual is continuously updated by the evolutionary process of B-cell receptor (BCR) mutation and selection. It has recently become possible to gain detailed information concerning this process through high-throughput sequencing. Here, we develop modern statistical molecular evolution methods for the analysis of B-cell sequence data, and then apply them to a very deep short-read dataset of BCRs. We find that the substitution process is conserved across individuals but varies significantly across gene segments. We investigate selection on BCRs using a novel method that side-steps the difficulties encountered by previous work in differentiating between selection and motif-driven mutation; this is done through stochastic mapping and empirical Bayes estimators that compare the evolution of in-frame and out-of-frame rearrangements. We use this new method to derive a per-residue map of selection, which provides a more nuanced view of the constraints on framework and variable regions.