Neurons in cortical area V4 respond selectively to complex visual patterns such as curved contours and non-Cartesian gratings. Most previous experiments in V4 have measured responses to small, idiosyncratic stimulus sets and no single functional model yet accounts for all of the disparate results. We propose that one model, the spectral receptive field (SRF), can explain many observations of selectivity in V4. The SRF describes tuning in terms of the orientation and spatial frequency spectrum and can, in principle, predict the response to any visual stimulus. We estimated SRFs for neurons in V4 of awake primates by linearized reverse correlation of responses to a large set of natural images. We find that V4 neurons have large orientation and spatial frequency bandwidth and often bimodal orientation tuning. For comparison, we estimated SRFs for neurons in primary visual cortex (V1). Consistent with previous observations, we find that V1 neurons have narrower bandwidth than that of V4. To determine whether estimated SRFs can account for previous observations of selectivity, we used them to predict responses to Cartesian gratings, non-Cartesian gratings, natural images, and curved contours. Based on these predictions, we find that the majority of neurons in V1 are selective for Cartesian gratings, whereas the majority of V4 neurons are selective for non-Cartesian gratings or natural images. The SRF describes visual tuning properties with a second-order nonlinear model. These results support the hypothesis that a second-order model is sufficient to describe the general mechanisms mediating shape selectivity in area V4.