The pharmaceutical industry has faced significant changes in recent years, primarily influenced by regulatory standards, market competition, and the need to accelerate drug development. Model-informed drug development (MIDD) leverages quantitative computational models to facilitate decision-making processes. This approach sheds light on the complex interplay between the influence of a drug’s performance and the resulting clinical outcomes. This comprehensive review aims to explain the mechanisms that control the dissolution and/or release of drugs and their subsequent permeation through biological membranes. Furthermore, the importance of simulating these processes through a variety of in silico models is emphasized. Advanced compartmental absorption models provide an analytical framework to understand the kinetics of transit, dissolution, and absorption associated with orally administered drugs. In contrast, for topical and transdermal drug delivery systems, the prediction of drug permeation is predominantly based on quantitative structure–permeation relationships and molecular dynamics simulations. This review describes a variety of modeling strategies, ranging from mechanistic to empirical equations, and highlights the growing importance of state-of-the-art tools such as artificial intelligence, as well as advanced imaging and spectroscopic techniques.