AlGaAs-on-insulator (AlGaAs-OI) is a new and promising material platform for integrated nonlinear photonics. In this work a new and robust fabrication process was developed at the University of Glasgow for low loss, high confinement AlGaAs-OI waveguides. By judiciously designing the waveguide geometry, phase-matching and dispersion engineering are demonstrated in these waveguides for second harmonic generation and supercontinuum generation, respectively. Using these designs, second harmonic generation is demonstrated for the first time in an AlGaAs-OI waveguide at telecommunication wavelengths, with a maximum internal normalised efficiency of 1202±55%W-1cm-2 achieved for a 100fs pulsed excitation wavelength at 1560nm. Supercontinua spanning 0.5 octaves (-30dB level) are also demonstrated, exhibiting a plethora of nonlinearities and propagation losses as low as 1.5dB/cm at telecommunication wavelengths. These results are of particular importance for enabling new chip-scale devices for sensing, metrology and quantum optics.