Throughout the last decades, Monte Carlo (MC) techniques have been used in simulating various complex systems. In this paper, we investigate how MC-based methods are used in the field of Drug Delivery, indicating what aspects of the complex problems of drug dissolution and design can benefit from this particular approach. After introducing the area of modelling drug dissolution, with its different features and needs, we report and examine the existing Direct MC and Stochastic Cellular Automata modelling efforts used to simulate dissolution of pharmaceutical compacts or related phenomena. In Part 2, we enlarge on a description of our work on Direct MC, for the particular case of simulating a binary system consisting of poorly soluble drug dispersed in a matrix of highly-soluble acid excipient.