A transgenic non-human vertebrate (e.g. a mouse) or non-human vertebrate cell comprises a gene locus for expression of antibody heavy chains, comprising a human variable region, an endogenous mu constant region, and a humanised non-mu (preferably gamma) constant region downstream of the mu constant region. The locus can express a chimeric IgM immunoglobulin comprising a human variable region and an endogenous mu constant region, and following in vivo isotype switching it can express a fully-human non-IgM (e.g. IgG) immunoglobulin comprising a human variable region and a human non-mu (e.g. gamma) constant region. The vertebrate or cell may express human heavy-chain only antibodies or it may also express human or chimeric light chain immunoglobulins. The animals or cells may be used to obtain antigen-specific antibodies that are fully human (i.e., comprising human variable and constant regions) and have undergone affinity maturation in vivo. The animal or cell may comprise a functional activation induced cytidine deaminase (AID) gene to enhance isotype switching. Populations of non-human vertebrates expressing human antibodies, and the pharmaceutical and therapeutic uses of antibodies produced in this way, are also provided.