As Moores law is gradually losing its effectiveness, developing alternative high-speed and low-energy-consuming information technology with post-silicon advanced materials is urgently needed. The successful application of tunneling magnetoresistance (TMR) in magnetic tunnel junctions (MTJs) has given rise to a tremendous economic impact on magnetic informatics, including MRAM, radio-frequency sensors, microwave generators and neuromorphic computing networks. The emergence of two-dimensional (2D) materials brings opportunities for MTJs based on 2D materials which have many attractive characters and advantages. Especially, the recently discovered intrinsic 2D ferromagnetic materials with high spin-polarization hold the promise for next-generation nanoscale MTJs. With the development of advanced 2D materials, many efforts on MTJs with 2D materials have been made both theoretically and experimentally. Various 2D materials, such as semi-metallic graphene, insulating h-BN, semiconducting MoS2, magnetic semiconducting CrI3, magnetic metallic Fe3GeTe2 and some other recently emerged 2D materials are discussed as the electrodes and/or central scattering materials of MTJs in this review. We discuss the fundamental and main issues facing MTJs, and review the current progress made with 2D MTJs, briefly comment on work with some specific 2D materials, and highlight how they address the current challenges in MTJs, and finally offer an outlook and perspective of 2D MTJs.