Sensory neurons can integrate their inputs nonlinearly, and this nonlinear pooling allows the extraction of complex features from the natural environment. Such nonlinear computations are ubiquitous in the visual system, and can be captured with encoding models that partition receptive fields into subunits whose outputs are nonlinearly combined. In the retina, the nonlinearities that transform subunit signals before integration by retinal ganglion cells affect the cells’ sensitivity to the spatial structure of natural scenes. Fitting subunit models to neural responses remains a challenge, as available solutions largely ignore integration nonlinearities. Here, we introduce the subunit grid method, which offers a generic parametrization of nonlinear subunit models and a stimulus that efficiently probes the subunit layout and that evokes reliable responses for effective parameter fitting. Using multielectrode-array recordings from the isolated mouse retina, we fit subunit grid models to spiking responses of ganglion cells under flashed gratings with varying spatial frequency and orientation. Fitted models capture nonlinear grating responses with small subunits that can display rectification or saturation to different degrees, even in the presence of a subunit surround. Additionally, subunit layouts and nonlinearities consistently differ between ganglion cell types. Compared to spatially linear models, subunit grids improve response predictions to both spatially structured artificial stimuli and natural images. Using data from rapidly flickering gratings, we extend our models to the time domain, and show improved response predictions to natural movies with imprinted mouse eye movements. Finally, we show that subunit grids can fit receptive fields with multiple inputs, such as the ON and OFF subunits of ON-OFF direction-selective retinal ganglion cells. Together, we introduce a novel method for mapping nonlinear receptive fields, showcase how subunit grids extend functional descriptions of neuronal types beyond linear receptive fields, and thereby reduce the gap in predicting the retinal output to natural visual inputs.