Two-dimensional (2D) materials are a new family of materials with interesting physical properties, ranging from insulating hexagonal boron nitride, semiconducting or semi-metallic transition metal dichalcogenides, to gapless metallic graphene. In this review, we provide a brief discussion of transport studies in transition metal dichalcogenides, including both semiconducting and semi-metallic phases, as well as a discussion of the newly emerged narrow bandgap layered material, black phosphorus, in terms of its electrical and quantum transport properties at room and cryogenic temperatures. Ultra-thin layered channel materials with atomic layer thickness in the cross-plane direction, together with relatively high carrier mobility with appropriate passivation techniques, provide the promise for new scientific discoveries and broad device applications.