Scientific and technological innovations of the last few decades in the field of wireless telecommunications and networking have enabled a wide area of applications and services in healthcare, transportation, environmental protection, infotainment, industrial automation, homeland security, smart urban environments and other disparate fields. At the same time the complexity and criticality of these systems creates many technical challenges in their design, development and operation. This paper reviews a number of important application fields of wireless communications and networking and discusses recent results, key challenges and unsolved issues in each one of them. It goes on to present some theoretical and practical issues and research directions in the field of wireless communications and networking that are common to most if not all application areas. These include theoretical link and network capacity limits, cognitive radio and cognitive networking, programming and in-field reprogramming of wireless devices, and complex system design inspired by biology and physics.