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Two-dimensional (2D) materials, such as graphene (Gr), transition metal dichalcogenides (TMDs) and hexagonal boron nitride (h-BN), offer interesting opportunities for the implementation of vertical transistors for digital and high-frequency electronics. This paper reviews recent developments in this field, presenting the main vertical device architectures based on 2D/2D or 2D/3D material heterostructures proposed so far. For each of them, the working principles and the targeted application field are discussed. In particular, tunneling field effect transistors (TFETs) for beyond-CMOS low power digital applications are presented, including resonant tunneling transistors based on Gr/h-BN/Gr stacks and band-to-band tunneling transistors based on heterojunctions of different semiconductor layered materials. Furthermore, recent experimental work on the implementation of the hot electron transistor (HET) with the Gr base is reviewed, due to the predicted potential of this device for ultra-high frequency operation in the THz range. Finally, the material sciences issues and the open challenges for the realization of 2D material-based vertical transistors at a large scale for future industrial applications are discussed.