► We review various types of Urban Transportation Network Design Problem (UTNDP). ► We focus on the topological design of urban transportation networks. ► We review studies on road network, transit network, and multi-modal network design. ► We propose possible future research directions for each type of UTNDP. This paper presents a comprehensive review of the definitions, classifications, objectives, constraints, network topology decision variables, and solution methods of the Urban Transportation Network Design Problem (UTNDP), which includes both the Road Network Design Problem (RNDP) and the Public Transit Network Design Problem (PTNDP). The current trends and gaps in each class of the problem are discussed and future directions in terms of both modeling and solution approaches are given. This review intends to provide a bigger picture of transportation network design problems, allow comparisons of formulation approaches and solution methods of different problems in various classes of UTNDP, and encourage cross-fertilization between the RNDP and PTNDP research.