Two-dimensional (2D) materials are under intensive investigation recently due to variety of electronic properties, ranging from insulators (h-BN) to semi-metals (graphene), semiconductors (MoS2, WSe2) with wide variability of band-gap and correlated phases (NbSe2, TaS2). Recently, focus of research has been moved from graphene, which is now a well understood material, towards less explored materials, in particular monolayers of semiconducting transition metal dichalcogenides (TMDCs) such as MoS2 with direct band-gap in optical range (1.5 - 2 eV) and potential towards scalable electronics applications immune to short channel effects. This thesis in fact explores materials beyond exfoliated MoS2 with the focus on electrical and structural properties of monolayers of WS2, ReS2 and synthesized by means of chemical vapour deposition (CVD) monolayers of MoS2, MoSe2 and WSe2. Four main chapters discuss the following aspects of these materials. Chapter 4 studies in details transport properties of monolayer WS2 for the first time. We demonstrate wide tuning of transport in this material from insulating regime through localized states to band-like transport with insulator to metal transition (MIT) in between, with mobilities = 50 cm2/Vs at room temperature. In Chapter 5 we employ electrolyte gating for fabrication of the first electric double-layer transistor (EDLT) based on monolayers and multilayers of ReS2. Furthermore, we employ this as a system for variation of electrostatic disorder and find an unusual and strong modulation in conduction band of ReS2. The discovered modulation of conductivity via controllable introduction of electrostatic disorder can help to understand this material as well as other ultrathin 2D systems and to optimize the design of devices based on them. In Chapter 6 we use atomically smooth sapphire for demonstration of the first epitaxial monolayer MoS2 growth. We can control the orientation of single-crystalline grains on the substrate and create large area continuous films, where grain boundaries between the grains have no impact on transport properties in contrast to other reports. Finally, Chapter 7 discusses further advances in CVD growth of TMDCs, with the first demonstration of ambipolar insulator to metal transition in devices, based on monolayers of MoSe2 and WSe2. In conclusion, this thesis establishes connection between transport properties of monolayers of 2D semiconductors and structural or electrostatic disorder. These results are important for both fundamental understanding of transport in two-dimensional materials and practical applications.