The responses of visual neurons, as well as visual perception phenomena in general, are highly nonlinear functions of the visual input, while most vision models are grounded on the notion of a linear receptive field (RF). The linear RF has a number of inherent problems: it changes with the input, it presupposes a set of basis functions for the visual system, and it conflicts with recent studies on dendritic computations. Here we propose to model the RF in a nonlinear manner, introducing the intrinsically nonlinear receptive field (INRF). Apart from being more physiologically plausible and embodying the efficient representation principle, the INRF has a key property of wide-ranging implications: for several vision science phenomena where a linear RF must vary with the input in order to predict responses, the INRF can remain constant under different stimuli. We also prove that Artificial Neural Networks with INRF modules instead of linear filters have a remarkably improved performance and better emulate basic human perception. Our results suggest a change of paradigm for vision science as well as for artificial intelligence.