In this work, we formulate NEWRON: a generalization of the McCulloch-Pitts neuron structure. This new framework aims to explore additional desirable properties of artificial neurons. We show that some specializations of NEWRON allow the network to be interpretable with no change in their expressiveness. By just inspecting the models produced by our NEWRON-based networks, we can understand the rules governing the task. Extensive experiments show that the quality of the generated models is better than traditional interpretable models and in line or better than standard neural networks.