Smart environments such as smart grid, smart transportation, smart buildings are upon us because of major advances in sensor, communication, cloud and other cyberphysical system technologies. The collective name for interconnected sensors, placed on "things" within fixed cyber-physical infrastructures, is Internet of Things (IoT). IoT enables cities and rural areas to become smarter and to offer new digital services and functions to diverse groups of users. However, IoT often represents interconnection of static things, which are builtin into the physical infrastructures of users' homes, offices, roads and other physical and critical infrastructures. In this paper, we analyze things that are mobile, and explore the space of Internet of Mobile Things (IoMT). Mobility of digital devices such as phones and vehicles has been with us for some time, but as the number of sensors in mobile devices increases, the density of mobile devices increases, and users' reliance on mobile devices increases, mobile things become very much an integral fabric of our smart environment. In this paper, our goal is to discuss challenges, selective designs and implementations of IoMT. We show the impact of mobility and the care we collectively have to take when designing the next generation of smart environments with mobile things in them.