Single-layer of molybdenum disulfide (MoS2) and other transition metal dichalcogenides appear to be promising materials for next generation nanoscale applications (optoelectronic and catalysis), because of their low-dimensionality, intrinsic direct band-gap in the visible spectrum, and strikingly large binding energies for excitons and trions. MoS2 is also known to be a leading hydrodesulphurization catalyst. In this talk I will present results which provide a framework for manipulating the functionality of these materials and take us closer to the goal of rational material design. One emphasis will be on catalytic properties of pure and defect-laden single layer MoS2 with and without underlying support, and with adsorbed metallic nanoparticles. Another will be on the binding energies of multiple excitations (excitons, trions, biexcitons) in single and bilayer (hetero and homo) transition metal dichalcogenides. I will also discuss the characteristics of ultrafast charge dynamics in these systems, response to a short laser pulse. *Work supported by DOE grants DE-FG02-07ER15842 and DE-FG02-07ER46354.