Parton Distribution Functions on the Lattice

I present a first direct lattice-QCD calculation of the x dependence of hadron structure functions. By taking a hadron with a large momentum boost, we are able to connect light-cone quantities to lattice-QCD nonlocal but time-independent matrix elements. Since the largest attainable momentum is limited, we correct for the sizable leading momentum dependence systematically. In this talk, I present an exploratory study of the nucleon quark density, helicity and transversity distributions, and pion distribution amplitudes.