In certain embodiments the present invention involves methods of killing tumor cells that comprise an oncogenic PDGFR mutation, and methods of treating subjects having tumors that comprise such tumor cells. In some embodiments such methods involve using PI3K inhibitors, or a combination of a PI3K inhibitor and an mTOR inhibitor, or a dual PI3K/mTOR inhibitor. The present invention also provides methods for determining whether a subject is a candidate for treatment, methods for evaluating the efficacy of treatment, and other methods, compositions, model systems, and assays.