The article is structured as follows: We begin with a brief account of the fundamental performance parameters of photodetectors for readers new to the field (see Box 1). We continue with a definition and distinction of extrinsic vs. intrinsic response times, discuss the effect of the TMDC layer thickness and provide a brief overview of the speed limiting factors in TMDC photodetectors. On this basis, we devise chemical and physical design strategies for accelerating their photoresponse, taking into account substrate considerations, chemical healing of defects, edge electrodes and reducing the photoresistance. We conclude with promising future directions to even faster photodetection, including optical cavities, the bulk photovoltaic effect and plasmonics.