The idea of a smart city is one that utilises Internet-of-Things (IoT) technologies and data analytics to optimise the efficiency of city operations and services, so as to provide a high quality of life for its citizens. Due to reduced public funding, many public transport systems are already facing challenges to maintain their services. For a smart city, the goal of public transport is not simply the movement of people, but the provision and enhancement of mobility for living. This will be particularly challenging due to changes in habitation trends and work patterns. For example, the growth of mega-cities has led to extreme traffic congestion in city centres and urban sprawl on their outskirts. In order to provide sufficient coverage and frequency of service, an integrated co-ordinated multi-modal public transport system is needed, leading to substantial increase in operational complexity. Environmental concerns and the recent pandemic may also change work and commuting patterns in the future, with more people working from home and companies adopting flexible work shifts. For smart cities, public transport must offer ubiquitous access, real-time response to demand, convenience and quality service, and energy-efficient operations. This paper will discuss the challenges in network design, operations planning, scheduling and management of smart public transport systems. A brief survey of recent research and innovations will also be presented.