We review recent achievements in the field of nanoscale nonlinear AlGaAs photonics based on all-dielectric optical antennas. After discussing the motivation and main technological challenges for the development of an AlGaAs monolithic platform for χ (2) nonlinear nanophotonics, we present numerical and experimental investigations of the second-order nonlinear response and physical reasons for high efficiency of second-order nonlinear interactions in the AlGaAs nano-antennas. In particular, we emphasize the role of the dipolar resonances at the fundamental frequency and the multipolar resonances at the second harmonic wavelength. We also discuss second-harmonic generation directionality and show possible strategies to engineer the radiation pattern of nonlinear antennas.