Popular notions of how the retina encodes visual stimuli typically focus on the center-surround receptive fields of retinal ganglion cells, the output neurons of the retina. In this view, the receptive field acts as a linear filter on the visual stimulus, highlighting spatial contrast and providing efficient representations of natural images. Yet, we also know that many ganglion cells respond vigorously to fine spatial gratings that should not activate the linear filter of the receptive field. Thus, ganglion cells may integrate visual signals nonlinearly across space. In this talk, I will discuss how these (and other) nonlinearities relate to the encoding of natural visual stimuli in the retina. Based on electrophysiological recordings of ganglion and bipolar cells from mouse and salamander retina, I will present methods for assessing nonlinear processing in different cell types and examine their importance and potential function under natural stimulation.