Practical applications implementing integrated photonic circuits can benefit from nonlinear optical functionalities such as wavelength conversion, all-optical signal processing, and frequency-comb generation, among others. Numerous nonlinear waveguide platforms have been explored for these roles; the group of materials capable of combining both passive and active functionalities monolithically on the same chip is III–V semiconductors. AlGaAs is the most studied III–V nonlinear waveguide platform to date; it exhibits both second- and third-order optical nonlinearity and can be used for a wide range of integrated nonlinear photonic devices. In this review, we conduct an extensive overview of various AlGaAs nonlinear waveguide platforms and geometries, their nonlinear optical performances, as well as the measured values and wavelength dependencies of their effective nonlinear coefficients. Furthermore, we highlight the state-of-the-art achievements in the field, among which are efficient tunable wavelength converters, on-chip frequency-comb generation, and ultra-broadband on-chip supercontinuum generation. Moreover, we overview the applications in development where AlGaAs nonlinear functional devices aspire to be the game-changers. Among such applications, there is all-optical signal processing in optical communication networks and integrated quantum photonic circuits.