The recent spectacular progress in the microelectronic, information, communication, material and sensor technologies created a big stimulus towards development of smart communicating cyber-physical systems (CPS) and Internet of Things (IoT). CPS and IoT are undergoing an explosive growth to a large degree related to advanced mobile systems like smart automotive and avionic systems, mobile robots and wearable devices. The huge and rapidly developing markets of sophisticated mobile cyber-physical systems represent great opportunities, but these opportunities come with a price of unusual system complexity, as well as, stringent and difficult to satisfy requirements of many modern applications. Specifically, smart cars and various wearable systems to a growing degree involve big instant data from multiple complex sensors or other systems, and are required to provide continuous autonomous service in a long time. In consequence, they demand a guaranteed (ultra-)high performance and/or (ultra-)low energy consumption, while requiring a high reliability, safety and security. To adequately address these demands, sophisticated embedded computing and embedded design technologies are needed. After an introduction to modern mobile systems, this paper discusses the huge heterogeneous area of these systems, and considers serious issues and challenges in their design. Subsequently, it discusses the embedded computing and design technologies needed to adequately address the issues and overcome the challenges in order to satisfy the stringent requirements of the modern mobile systems.