Alkylation of isobutane with C-3-C-5 olefins currently produces alkylates that are the highest-quality and cleanest-burning gasolines. Four processes are widely used; two employ sulfuric acid as the catalyst, whereas the other two employ liquid HF. Processes that employ solid catalysts have yet to be commercialized. This paper comprises a review of recent findings concerning the fundamentals (chemistry of alkylation plus side reactions, mass- and heat-transfer steps in the acid/hydrocarbon dispersions, characteristics of dispersion, etc.), i.e., the physicochemical events. A sequence of over 30 chemical, physical, and transfer steps is outlined and explained, for probably the first time. Better understanding of the fundamentals strongly suggests that much improved processes can be developed.