In recent usage, quasi-Monte Carlo methods performed much better than the classical theory tells us. In order to study the phenomenon of high-dimensional quasi-Monte Carlo integration systematically, we use the notion of tractability, strong tractability and weak tractability, which are desired properties of integration problems. We investigate whether simple tensor product spaces and weighted spaces fulfil the requirements of polynomial tractability. In case of strong polynomial tractability, the convergence order is independent of the dimension. Moreover, we study tractability of the classical star discrepancy.