We find that, although inversion noise has only a marginal effect on the linewidth of a semiconductor laser in CW operation, in the presence of dynamics it may play a key role in determining the final dynamical state. It is therefore essential to include both field noise and carrier noise of realistic strength when analysing semiconductor laser dynamics. Next we investigate the influence of quantum noise, both field and carrier noise, on the highly complex nonlinear dynamics that arise in a single-mode semiconductor laser subject to filtered optical feedback. Our numerical study based on stochastic rate equations shows that for a wide range of filter widths the noise may lead to qualitatively different dynamics than predicted by a deterministic analysis. In particular, we find that certain attractors that are predicted in the absence of noise may no longer be available when the effects of noise are correctly incorporated, while others show remarkable robustness instead. In general, the results confirm that carrier noise in the laser can influence the dynamics quite substantially. Finally, we present numerical results of noise-induced pulsations in a semiconductor laser with optical injection. We show that, close to the locking edge, patterns of single, two and three pulses can be excited and we suggest that experimental study of this multi-pulse excitability be based on pulse timing statistics.