In this manuscript, we will theoretically compute and experimentally investigate the dynamics of an optically injected nanostructure laser as a function of the injection strength and the optical detuning frequency. A model describing the optically-injected semiconductor laser is derived in dimensionless format that accounts for the large nonlinear gain component associated with nanostructure semiconductor lasers through the gain coefficient's derivative with respect to perturbations in the carrier and photon density. The nonlinear gain (carrier) relaxation rate and gain compression coefficient account for the perturbation in the slave laser's photon density, and are theoretically shown to have a strong impact on the level of stability exhibited by the optically-injected laser. The theoretical model is experimentally verified through the optical-injection of a quantum-dash Fabry-Perot laser at an operating wavelength of 1550 nm. The quantum-dash laser's large damping rate and sufficiently small linewidth enhancement factor are observed to inhibit period-doubling and chaotic operation under zero frequency-detuning conditions. Additionally, the optically injected quantum-dash laser is found to exhibit a large period-one operational state as the injection strength and the detuning frequency are varied, resulting in a highly tunable microwave frequency in the coupled system's equilibrium state. The enhanced and undamped relaxation oscillations of the period-one state are discussed as a building block for tunable photonic oscillators in various RF photonics applications. Finally a path towards realizing an optically-injected diode laser with a THz resonance frequency will be reviewed.