Moving walkways (MW) have been imagined as a possible means of transport since the late 19th century, and this system has fascinated urban planners and engineers ever since. Contrary to what has been imagined, moving walkways are only used in transportation hub corridors, and not as a main transport mode in city centers. Today however, MWs are receiving increasing attention as a possible solution to congestion and pollution, as well as a catalyst for soft mobility. This paper explores the role of moving walkways as a transport system, and it presents an optimized design of a network of MWs in a city center. We review historical MWs, current installations and future possibilities, using different perspectives, from geography to urban planning to transport engineering. We discuss the way in which MWs influence how people inhabit the urban space, and we review this system in the context of history of urban planning. Then, we describe a technological development called accelerating moving walkways (AMW), i.e. MWs able to reach a higher speed than traditional ones. We develop an optimization framework to design a network of AMWs, and we apply it to a real case study. The results of the network design are a reference useful to discuss the feasibility of the system starting from an engineering perspective. We conclude that the use of MWs can facilitate the flexibility and spontaneity typical of pedestrian movements, and this system could be integrated in the mix of urban transport modes in city centers.