Two-dimensional (2D) materials have attracted extensive interest due to their excellent electrical, thermal, mechanical, and optical properties. Graphene has been one of the most explored 2D materials. However, its zero band gap has limited its applications in electronic devices. Transition metal dichalcogenide (TMDC), another kind of 2D material, has a nonzero direct band gap (same charge carrier momentum in valence and conduction band) at monolayer state, promising for the efficient switching devices (e.g., field-effect transistors). This review mainly focuses on the recent advances in charge carrier mobility and the challenges to achieve high mobility in the electronic devices based on 2D-TMDC materials and also includes an introduction of 2D materials along with the synthesis techniques. Finally, this review describes the possible methodology and future prospective to enhance the charge carrier mobility for electronic devices.