Modern biomedical research requires access to high quality specimens of human tissue with or without extensive clinical annotation. Multiple types of organizations have developed to supply human tissues to support biomedical research. These organizations follow different models including the specific models of 1) prospective collection, 2) tissue banking, and 3) tissue collection associated with clinical trials as well as the model of 4) a tissue resource that incorporates features of the other models. These types of organizations devoted to supplying tissues for research have chosen different goals to meet the different tissue and informational needs of the investigators to whom they supply tissue. In order to provide high quality tissues to support research, all models should rely on a strong quality assurance program with extensive quality control of the tissues being provided to support research. In addition to facilities which collect, process, store and provide tissues, the need for a rigorous QA program applies to all resources and infrastructures used to support biomedical research. The UAB Tissue Collection and Banking Facility which provides human tissue to support biomedical research has been functioning and developing since 1979. To our knowledge, similar programs in providing tissues from animals are less developed, but could easily follow the models which UAB and other institutions providing human tissues have established, including the approaches of UAB and others to QA and QC. This manuscript reviews the current concepts of QA and QC in use in organizations supplying tissue to support biomedical research as well as new approaches in QA and QC that have been proposed.