A method for generating or expanding a population of T cells specific for a virus by a method comprising: stimulating T cells by culture in the presence of antigen presenting cells (APCs) presenting a peptide of the virus, wherein at least 10% of the media in which the cells are cultured is conditioned media obtained from a stimulation culture comprising T cells and APCs presenting a peptide of the virus. Also disclosed are methods for accelerating the rate of expansion of a virus-specific T cell population, and methods for treating or preventing diseases or disorders using the generated or expanded T cell population.