Molecular computing is a discipline that aims at harnessing individual molecules at nanoscales to perform computations. The best studied molecules for this purpose to date have been DNA and bacteriorhodopsin. Biomolecular computing allows one to realistically entertain, for the first time in history, the possibility of exploiting the massive parallelism at nanoscales for computational power. This talk will discuss major achievements to date, both experimental and theoretical, as well as challenges and major potential advances in the immediate future.