Shared Mobility Systems (SMS) facilitate on-demand journeys using one or more transporta- tion modes such as car-sharing, bike-sharing, or ride-sharing. As a result, SMS often face challenges such as finding suitable facility locations, efficient routing of shared vehicles, matching and re-distributing available resources with dynamic demands. Most existing surveys study how a particular challenge is addressed using artificial intelligence, machine learning, and optimisation techniques. However, these surveys fail to address the crucial ??Whole System Design' point of view, which includes the ??whole system' of interconnected stakeholders, entities, and subsystems that participate in, impact, and influence the success of each other and system a whole. Such a survey is highly required with the growing demand for flexible SMS that supports autonomous decision-making and offers multi-modal and inter-operable transportation services catered for highly dynamic traffic conditions in urban areas. This paper attempts to fill this gap by categorising the SMS' interconnected challenges in different transportation modes and reviewing how offered solutions across all modes address these challenges as a unified system.