Upon encountering an antigen, antibodies mature through various rounds of somatic mutations, resulting in higher affinities and specificities to the particular antigen. We review recent progress in four areas of antibody maturation studies. (1) Next-generation and single-cell sequencing have revolutionized the analysis of antibody repertoires by dramatically increasing the sequences available to study the state and evolution of the immune system. Computational methods, including machine learning tools, have been developed for reconstituting antibody clonal lineages and for general repertoire analysis. (2) The availability of X-ray structures, thermodynamic and kinetic data, and molecular dynamics simulations provide information on the biophysical mechanisms responsible for improved affinity. (3) In addition to improved binding to a specific antigen, providing affinity-independent diversity and self/nonself discrimination are fundamental functions of the immune system. Recent studies, including X-ray structures, yield improved understanding of both mechanisms. (4) Results from in vivo maturation help to develop methods of in vitro maturation to improve antibody properties for therapeutic applications, frequently combining computational and experimental approaches.