The Shared Mobility Problems (SMP) with the rideshare concept based on sharing a vehicle are fast becoming a trend in many urban cities around the world. Examples of these problems are like ridesharing, carpooling, taxisharing, buspooling, vanpooling, and multi-modal ridesharing. This is the new way to access transportation services by those who are propelling the sharing economy, where access rather than ownership is the new norm. This paper provides a systematic review of SMP using the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analysis) method. A total of 110 papers from the last decade are selected from 12 abstracts and citation databases to be reviewed and classified. This is done based on the problem types, variants, characteristics, and solution approaches. The current trends and analysis of the survey findings are also summarised. From this systematic review, it is observed that both the time window and multi-objective problems are popular among the researchers, while the minimisation of the total cost is the main concern in the literature of the SMP. Both static and dynamic cases of the SMP are the most researched where heuristic and metaheuristic approaches are widely adopted by the researchers in the literature. Finally, challenges and suggestions for future work are discussed and highlighted.