Since their modern debut in 2004, 2-dimensional (2D) materials continue to exhibit scientific and industrial promise, providing a broad materials platform for scientific investigation, and development of nano- and atomic-scale devices. A significant focus of the last decade's research in this field has been 2D semiconductors, whose electronic properties can be tuned through manipulation of dimensionality, substrate engineering, strain, and doping (Mak et al 2010 Phys. Rev. Lett. 105 136805; Zhang et al 2017 Sci. Rep. 7 16938; Conley et al 2013 Nano Lett. 13 3626─30; Li et al 2016 Adv. Mater. 28 8240─7; Rhodes et al 2017 Nano Lett. 17 1616─22; Gong et al 2014 Nano Lett. 14 442─9; Suh et al 2014 Nano Lett. 14 6976─82; Yoshida et al 2015 Sci. Rep. 5 14808). Molybdenum disulfide (MoS2) and tungsten diselenide (WSe2) have dominated recent interest for potential integration in electronic technologies, due to their intrinsic and tunable properties, atomic-scale thicknesses, and relative ease of stacking to create new and custom structures. However, to go 'beyond the bench', advances in large-scale, 2D layer synthesis and engineering must lead to 'exfoliation-quality' 2D layers at the wafer scale. This roadmap aims to address this grand challenge by identifying key technology drivers where 2D layers can have an impact, and to discuss synthesis and layer engineering for the realization of electronic-grade, 2D materials. We focus on three fundamental areas of research that must be heavily pursued in both experiment and computation to achieve high-quality materials for electronic and optoelectronic applications.