Main articles: T cell and B cell. T cells (thymus cells) and B cells (bone marrow-or bursa-derived cells) are the major cellular components of the adaptive immune response. T cells are involved in cell-mediated immunity, whereas B cells are primarily responsible for humoral immunity (relating to antibodies). The function of T cells and B cells is to recognize specific ânon-selfâ antigens, during a process known as antigen presentation.