The development of silicon semiconductor technology has produced breakthroughs in electronics-from the microprocessor in the late 1960s to early 1970s, to automation, computers and smartphones-by downscaling the physical size of devices and wires to the nanometre regime. Now, graphene and related two-dimensional (2D) materials offer prospects of unprecedented advances in device performance at the atomic limit, and a synergistic combination of 2D materials with silicon chips promises a heterogeneous platform to deliver massively enhanced potential based on silicon technology. Integration is achieved via three-dimensional monolithic construction of multifunctional high-rise 2D silicon chips, enabling enhanced performance by exploiting the vertical direction and the functional diversification of the silicon platform for applications in opto-electronics and sensing. Here we review the opportunities, progress and challenges of integrating atomically thin materials with silicon-based nanosystems, and also consider the prospects for computational and non-computational applications.