We provide an overview on patter formation in nonlinear, weakly-correlated, wave systems. We show that a weakly-correlated wavefront propagating in a non-instantaneous self-focusing medium undergoes modulation instability and breaks up into stripes and dots forming ordered incoherent structures of quasi-solitons. At higher nonlinearities, these quasi-solitons attract, and form clusters (aggregates) of solitons. Finally, we present very recent results on the first experimental observation of pattern formation and modulation instability in a cavity with incoherent light.