Since the invention of the metal-oxide-semiconductor field-effect transistor (MOSFET) in late 1959, the impact of electronics on human society has been increasingly pervasive, heavily regulating modern health, transport, finance, entertainment, and social media sectors through "Big Data." However, daily generation of petabytes of data from these sectors, along with their associated communication overhead, is placing an immense strain on the conventional computing and communication technologies, which were not developed exclusively for big data. Tackling these problems calls for a holistic overhaul of the current semiconductor technology, from materials to architecture, and two-dimensional (2D)-layered materials with their exotic electrical and structural properties are well positioned to accomplish just that. This perspective article aims to provide an overview of the key technological innovations in the nanoelectronics domain that have been achieved with 2D-materials thus far, and to bring forth the promise of this new materials family in developing brain-inspired ultra low-energy on-chip computing and communication techniques to usher a new era in electronics.