Public transport provision requires substantial organisational efforts, careful planning, financial contributions from the public, and coordination between millions of passengers and staff members in large systems. Efficient resource allocation is critical in its daily operations. Therefore, public transport has been among the most popular subjects in transport economics since the infancy of this discipline. This paper presents an overview of the literature developed over the past half century, including more than 300 important contributions. With a strong methodological orientation, it collects, classifies, and compares the frequently used analytical modelling techniques, thus providing a cookbook for future research and learning efforts. We discuss key findings on optimal capacity provision, pricing, cost recovery and subsidies, externalities, private operations, public service regulation, and cross-cutting subjects, such as interlinks with urban economics, political economy, and emerging mobility technologies.