The rise of research into shared mobility systems reflects emerging challenges, such as rising traffic congestion, rising oil prices and rising environmental concern. The operations research community has turned towards more sharable and sustainable systems of transportation. Shared mobility systems can be collapsed into two main streams: Those where people share rides and those where parcel transportation and people transportation are combined. This survey sets out to review recent research in this area, including different optimization approaches, and to provide guidelines and promising directions for future research. It makes a distinction between prearranged and real-time problem settings and their methods of solution, and also gives an overview of real-case applications relevant to the research area.