Edge-emitting mode-locked quantum-dot (QD) lasers are compact, highly efficient sources for the generation of picosecond and femtosecond pulses and/or broad frequency combs. They provide direct electrical control and footprints down to few millimeters. Their broad gain bandwidths (up to 50 nm for ground to ground state transitions as discussed below, with potential for increase to more than >200 nm by overlapping ground and excited state band transitions) allow for wavelength-tuning and generation of pico- and femtosecond laser pulses over a broad wavelength range. In the last two decades, mode-locked QD laser have become promising tools for low-power applications in ultrafast photonics. In this article, we review the development and the state-of-the-art of edge-emitting mode-locked QD lasers. We start with a brief introduction on QD active media and their uses in lasers, amplifiers, and saturable absorbers. We further discuss the basic principles of mode-locking in QD lasers, including theory of nonlinear phenomena in QD waveguides, ultrafast carrier dynamics, and mode-locking methods. Different types of mode-locked QD laser systems, such as monolithic one- and two-section devices, external-cavity setups, two-wavelength operation, and master-oscillator power-amplifier systems, are discussed and compared. After presenting the recent trends and results in the field of mode-locked QD lasers, we briefly discuss the application areas.