Transition-metal dichalcogenides (TMDCs) are important class of two-dimensional (2D) layered materials for electronic and optoelectronic applications, due to their ultimate body thickness, sizable and tunable bandgap, and decent theoretical room-temperature mobility of hundreds to thousands cm2/Vs. So far, however, all TMDCs show much lower mobility experimentally because of the collective effects by foreign impurities, which has become one of the most important limitations for their device applications. Here, taking MoS2 as an example, we review the key factors that bring down the mobility in TMDC transistors, including phonons, charged impurities, defects, and charge traps. We introduce a theoretical model that quantitatively captures the scaling of mobility with temperature, carrier density and thickness. By fitting the available mobility data from literature over the past few years, we are able to obtain the density of impurities and traps for a wide range of transistor structures. We show that interface engineering such as oxide surface passivation, high-k dielectrics and BN encapsulation could effectively reduce the impurities, leading to improved device performances. For few-layer TMDCs, we analytically model the lopsided carrier distribution to elucidate the experimental increase of mobility with the number of layers. From our analysis, it is clear that the charge transport in TMDC samples is a very complex problem that must be handled carefully. We hope that this Review can provide new insights and serve as a starting point for further improving the performance of TMDC transistors.