The search for a theory that explains the origin of galaxies and large-scale structure in the Universe is at an exciting stage. Observational advances, including measurements of the anisotropy in the cosmic microwave background and systematic surveys of galaxy redshifts, are confronting theoretical calculations of the distribution of matter produced by the action of gravity on small initial density fluctuations in the expanding Universe. Although the basic idea behind most theoretical models is simple, the details are complicated and there are many unknown parameters, such as the quantity and type of dark matter forming the bulk of the mass of the Universe. Consequently, at present, there are a number of contenders for a theory of structure formation but no single model can fit all the observational data completely satisfactorily.