The BK polyomavirus (BKPyV) is one of the main human polyomaviruses. After primary infection, it establishes a persistent infection, and acts as an opportunistic pathogen, innocuous in immunocompetent hosts, but causing potentially serious pathology in the context of immunosuppression, in particular in kidney and hematopoietic stem cell graft recipients. Much progress has been made in recent years in the description of virus-cell interactions, but many aspects of viral physiopathology remain mysterious, principally due to the asymptomatic nature of infection in immunocompetent individuals and the lack of an animal model. The characteristics of the antiviral immune response are beginning to become more clearly understood, particularly in kidney transplant patients. Work in these areas is important in order to identify patients at high risk of developing a severe infection. Indeed, in the absence of an effective antiviral therapy few therapeutic options are available, and patient management remains based on modulation of immunosuppressive therapy.