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Appropriate public transport systems are crucial in modern cities. Given the high costs that they represent and the impact they have on people's lives, effective tools are required to support their design. With this in mind, the Transit Network Design problem (TNDP) and the Transit Network Design and Frequency Setting problem (TNDFSP) have been extensively studied in the domain of Operations Research. However, due to the complexity of these problems, multiple simplifications are typically made when modelling and designing solution algorithms. Therefore, still no optimization techniques are available to address these problems in practice. Moreover, different studies address different versions of the problem, with varying assumptions and constraints, complicating the comparison of results or solution approaches. This paper presents an extensive survey of studies addressing the TNDP and the TNDFSP. It discusses the different assumptions, constraints, objectives, solutions approaches and testing instances that have been considered in the literature. Furthermore, a detailed analysis is done regarding the case studies considered for the TNDFSP. Moreover, the variants of the passenger assignment subproblem that have been applied within the TNDP and the TNDFSP are discussed. The analysis shows that extensive research has been done regarding these problems. However, it also identified the significant gap that still exists between theory and practice, even in the studies addressing case studies.

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