A review is presented of a range of investigations of the CW, self-pulsating and exci- table behaviour of blue-violet InGaN lasers with different designs of saturable absorber. Bi furcations have been identified that are the origin of the phenomena and different device designs are considered that are intended to control the laser behaviour in BD applications. It is found that the properties of the saturable absorber strongly affect the self-pulsation and excitability properties of the lasers. The influence on laser dynamics of other device and material parameters has also been investigated. Very encouraging agreement between the results of numerical calculations and the experimental data on self-pulsating laser operation is demonstrated.