It is foreseeable that any object in the near future will have an Internet connection—this is the Internet of Things vision. All these objects will be able to exchange and process information, most of them characterized by small size, power constrained, small computing and storage resources. In fact, connecting embedded low-power devices to the Internet is considered the biggest challenge and opportunity for the Internet. There is a strong trend of convergence towards an Internet-based solution and the 6LoWPAN may be the convergence solution to achieve the Internet of Things vision. Wireless mesh networks have attracted the interest of the scientific community in recent years. One of the key characteristics of wireless mesh networks is the ability to self-organize and self-configure. Mesh networking and mobility support are considered crucial to the Internet of Things success. This paper surveys the available solutions proposed to support routing and mobility over 6LoWPAN mesh networks.