The incorporation of Si1-xGex alloy heterostructures into conventional Si processes has been proposed as a means of improving the operating frequency and overall performance of Si field effect transistors. One parameter expected to benefit from this approach is the hole mobility, which would have important implications for high speed CMOS applications. Measured values of the hole mobility, however, have failed to live up to early expectations, and much ongoing research is directed at understanding whether this is an intrinsic limitation (e.g. due to alloy disorder scattering), or due to imperfections arising in the growth and fabrication process. In this thesis, a detailed theoretical study is presented of the hole mobility in single sub-band Si1-xGex heterostructures.