We experimentally studied the transport properties of ultracold bosonic atoms trapped ina disordered optical lattice|a system described by the disordered Bose-Hubbard model,which is a paradigm important to condensed matter physics. The disorder is created usinga controllable and completely characterizedne-grained optical speckleeld that is superimposedon 87Rb atoms con ned in a three-dimensional lattice in the strongly correlatedregime. We discovered that above a critical disorder strength, the gas of atoms transformsfrom a superuid to a disordered insulator. We compare our results to recent quantumMonte-Carlo numerical simulations of this model. Finally, I present an algorithm we inventedthat allows the pro le of laser beams to be shaped holographically into arbitraryintensity patterns suitable for trapping ultracold atoms.