Growing semiconductor laser sources on silicon is a crucial but challenging technology for developing photonic integrated circuits (PICs). InAs/GaAs quantum dot (Qdot) lasers have successfully circumvented the mismatch problem between III–V materials and Ge or Si, and have demonstrated efficient laser emission. In this paper, we review dynamical characteristics of Qdot lasers epitaxially grown on Ge or Si, in comparison with those of Qdot lasers on native GaAs substrate. We discuss properties of linewidth broadening factor, laser noise and its sensitivity to optical feedback, intensity modulation, as well as mode locking operation. The investigation of these dynamical characteristics is beneficial for guiding the design of PICs in optical communications and optical computations.