The discovery of two-dimensional (2D) materials has opened up new frontiers and challenges for exploring fundamental research. Recently, single-layer (SL) transition metal dichalcogenides (TMDCs) have emerged as candidate materials for electronic and optoelectronic applications. In contrast to graphene, SL TMDCs have sizable band gaps that change from indirect to direct in SLs, which is useful in making thinner and more efficient electronic devices, such as transistors, photodetectors, and electroluminescent devices. In addition, SL TMDCs show strong spin-orbit coupling effects at the valence band edges, giving rise to the observation of valley-selective optical excitations. Here, we review the basic electronic and optical properties of pure and defected group-VIB SL TMDCs, with emphasis on the strong excitonic effects and their prospect for future optoelectronic devices.