The present invention relates to engineered outer domain (eOD) immunogens of HIV gp120 and mutants thereof and methods of making and using the same. The present invention also includes fusions of eOD to various protein multimers to enhance immunogenicity. The mutant eODs bind to neutralizing antibody precursors. The mutant eODs can activate germline precursors on the pathway to eliciting a broadly neutralizing antibody (bnAb) response. The invention also relates to immunized knock-in mice expressing germline-reverted heavy chains. Induced antibodies showed characteristics of bnAbs and mutations that favored binding to near-native HIV-1 gp120 constructs. In contrast, native-like immunogens failed to activate precursors. The invention also relates to rational epitope design that can prime rare B cell precursors for affinity maturation to desired targets.