Public transit is a vast, interconnected systems design problem: coordinating numerous routes, frequencies , vehicles, operators, signals and passengers with uncertain demand and travel times. Operations Research (OR) brings a rich and mature arsenal of tools to tackle these issues. This report brings together 18 published and preprint papers which we have reviewed individually in six student-focussed sections that all bring OR to design of bus routes, timing of signals, quality of service, scheduling of vehicles and crews, demand-responsive transit, gig transportation, bike sharing, and electric vehicle fleet management. We cluster the papers into five categories and compare the OR techniques, which include calculus-based optimisation, mixed-integer, and set-partitioning programming, column-generation, and decomposition, genetic, and large-neighbourhood-search heuristics, robust optimisation, queueing, and stochastic-process models, Markov decision processes, and simulation. Three broad insights stand out. The first is the near-exclusive use of large-scale heuristics for bigger problems versus exact algorithms for smaller problems. The second is the treatment of demand and supply uncertainties as part of the decision making rather than as a post-hoc model refinement. The third is the real improvements, which are measured relative to different baselines on different case studies. We conclude by addressing limitations in the literature as well as in our review.