The successful isolation of a single-layer two-dimensional (2D) material (i.e. graphene) in 2004 has led to remarkable scientific discoveries and attracted tremendous research interests arising from its exceptional properties. Within just a few years, intensive research activities have been conducted on layered 2D materials, in particular, apart from graphene, transition metal dichalcogenides, for a variety of applications from electronics to biochemical sensing. Despite the rapid development in 2D materials research, many challenges and opportunities remain unexplored for devices based on such materials. This thesis addresses several emergent issues that impede the use of graphene and molybdenum disulphide (MoS2) for electronic applications: (1) large contact resistance in graphene devices, (2) Fermi level pinning in MoS2 devices, and (3) threshold voltage control in MoS2 transistors. (Abstract shortened by UMI.)