The discovery of two-dimensional (2D) material graphene has opened a door towards a class of layered novel nanomaterials with unique photonic and optoelectronic properties. Recently many new 2D materials have been reported, including topological insulators (TIs), transition metal dichalcogenides (TMDs) and black phosphorus (BP). These materials have been demonstrated high optical nonlinearity and Pauli blocking used as saturable absorbers (SAs) in pulsed lasers. In this paper, we summarize the current specifications from these 2D materials based mode-locked and Q-switched lasers. The laser performance in operating wavelength, optical bandwidth, repetition rate and pulse energy is reviewed. Finally future perspective is suggested. •Mode-locked and Q-switched lasers based on three 2D materials are reviewed.•Best specifications of bandwidth, repetition rate and pulse energy are summarized.•Material basic properties, fabrication and characterization are also introduced.