This Progress Report highlights recent developments in nanostructured organic and hybrid solar cells. The authors discuss novel approaches to control the film morphology in fully organic solar cells and the design of nanostructured hybrid solar cells. The motivation and recent results concerning fabrication and effects on device physics are emphasized. The aim of this review is not to give a summary of all recent results in organic and hybrid solar cells, but rather to focus on the fabrication, device physics, and light trapping properties of nanostructured organic and hybrid devices.