Provided are methods of producing an isolated T memory stem cell population, the method comprising a) isolating nave T cells from a mammal, wherein the mammal is not a mouse; b) activating the nave T cells and expanding the numbers of nave T cells in the presence of one or more non-specific T cell stimuli, one or more cytokines, and a GSK-3beta inhibitor. Also provided are methods of producing an isolated T memory stem cell population, the method comprising a) isolating lymphocytes from a mammal; b) sorting the lymphocytes using flow cytometry into a population comprising a phenotype comprising i) CD95+, CD45RO−, and CCR7+; and ii) CD62L+ or one or more of CD27+, CD28+, CD45RA+, and CD127+ to produce an isolated T memory stem cell population. Further embodiments of the invention provide related cells, populations of cells, pharmaceutical compositions, and methods of treating or preventing cancer.