Optical nanoantennas loaded by nanoparticles are used to provide large and controllable field enhancement at the nanoscale. Here we show how the introduction of nonlinearities at the nanoload may realize a whole set of all-optical nanoscale functionalities, such as memories, switches and transistors, as a function of whether the nanoantenna is excited "below" or "above" its resonance frequency. After discussing the main features of this nonlinear nanoantenna operation, we employ its bistable and self-tunable response in a planar array design, which may constitute different nonlinear devices and functionalities of significant interest for optical computing applications.