The Brønsted acidity of proton-exchanged zeolites has historically led to the most impactful applications of these materials in heterogeneous catalysis, mainly in the fields of transformations of hydrocarbons and oxygenates. Unravelling the mechanisms at the atomic scale of these transformations has been the object of tremendous efforts in the last decades. Such investigations have extended our fundamental knowledge about the respective roles of acidity and confinement in the catalytic properties of proton exchanged zeolites. The emerging concepts are of general relevance at the crossroad of heterogeneous catalysis and molecular chemistry. In the present review, emphasis is given to molecular views on the mechanism of generic transformations catalyzed by Brønsted acid sites of zeolites, combining the information gained from advanced kinetic analysis, in situ, and operando spectroscopies, and quantum chemistry calculations. After reviewing the current knowledge on the nature of the Brønsted acid sites themselves, and the key parameters in catalysis by zeolites, a focus is made on reactions undergone by alkenes, alkanes, aromatic molecules, alcohols, and polyhydroxy molecules. Elementary events of C-C, C-H, and C-O bond breaking and formation are at the core of these reactions. Outlooks are given to take up the future challenges in the field, aiming at getting ever more accurate views on these mechanisms, and as the ultimate goal, to provide rational tools for the design of improved zeolite-based Brønsted acid catalysts.