This article reviews the potential of graphene and related two-dimensional (2D) materials for applications in micro- and nanoelectronics. In addition to graphene, special emphasis is placed on transition metal dichalcogenides (TMDs). First, we discuss potential solutions for application-scale material growth, in particular chemical vapor deposition. We describe challenges for electrical contacts and dielectric interfaces with 2D materials. The device-related sections in this review first weigh the pros and cons of semi-metal graphene as a field-effect transistor (FET) channel material for logic and radio frequency applications. This is followed by an introduction to alternate graphene switch concepts that utilize the particular properties of the material, namely tunnel FETs, vertical devices, and bilayer pseudospin FETs. The final section is dedicated to semiconducting TMDs and their integration in FETs using the examples of n-type molybdenum disulfide (MoS2) and p-type tungsten diselenide (WSe2).