This thesis work focuses on the design, fabrication and measurement of Gallium Arsenide (GaAs) nano-optomechanical disk resonators. These disks are both GHz frequency mechanical resonators, and high Q (>10^5) optical whispering gallery mode resonators. By confining optical and mechanical energy on a sub-µm^3 volume, they enable extremely large optomechanical coupling strengths (g0>1 MHz). We present the technological developments which enabled the integration of these resonators with optical coupling waveguides directly on a semiconductor chip, while maintaining state of the art performance. We discuss the different optomechanical coupling mechanisms (radiation pressure, photoelasticity) in GaAs disks, as well as the sources of optical and mechanical dissipation in these resonators. We present as well optomechanical experiments in air and in a cryostat at low temperature, which go from the measurement of Brownian motion and the observation of dynamical back-action, to the first attempts to approach the quantum regime of mechanical displacement. Finally, we present an additional nano-optomechanical development carried out on the silicon nitride (SiN) platform, which lead to the fabrication of high Q on-chip whispering gallery mode resonators. After the study of the optical instability and self-pulsing dynamics of these resonators, we present the first signatures of dissipative optomechanical coupling in these systems.
