The promotion of urban mobility by integrating people-and-goods transportation has attracted increasing attention in recent years. Within this framework, diversified forms such as co-modality, freight on transit, and crowdshipping have been proposed, piloted or implemented. The success of the implementation and market penetration depends on not only the novelties of the concept but also the planning and operational efficiency. Thus, a comprehensive review focusing on the operation of integrated people-and-goods transportation systems and associated critical decisions and subproblems is performed. Different practical forms in which people and goods are transported in an integrated manner are identified. The critical decisions associated with each form and subproblem are discussed, along with corresponding models and solution approaches. Notably, because integrated transportation systems are in the early exploration stage at present, new forms are expected to emerge. Therefore, this paper proposes a general framework to realise the planning and operation of new forms in the future. The decisions and subproblems identified from existing forms are fed to the proposed general framework to identify two key research opportunities: to improve or extend existing research and to conduct pioneering research to fill the gaps in the frameworks for operating potential forms of integrated people-and-goods transportation.