Chaotic semiconductor laser diodes can be used to precipitate secure communications schemes via synchronisation of two such lasers [75]. We study various sets of ordinary differential equations that are used to model such semiconductor laser diodes. We begin by extending the bifurcation analysis ofDubbeldam and Krauskopf [23] to dimensionless equations derived from the Yamada model [91] with terms representative of spontaneous emission and diffusion effects included. We show that the bifurcation diagram changes dramatically at a certain diffusion level, but that the region of self-pulsation is still delineated by the Hopf bifurcation curve. Other models [79, 83] which include recombination effects are also considered. The excitable region of the parameter space of the dimensionless equations derived from the Yamada model with diffusion effects neglected is considered, and approximations of the excitability threshold are derived. Finally, chaotic behaviour arising from sinusoidal modulation of the pump cunent is analysed. Lyapunov exponent calculations are supplemented with a return map analysis in order to distinguish between periodic motion and chaos as the modulation depth and frequency are varied. The presence or otherwise of chaos is related to the bifurcation analysis and dominant resonant frequency of the unmodulated laser diode.