Mobile communications have been undergoing a generational change every ten years or so. However, the time difference between the so-called "G's" is also decreasing. While fifth-generation (5G) systems are becoming a commercial reality, there is already significant interest in systems beyond 5G, which we refer to as the sixth-generation (6G) of wireless systems. In contrast to the already published papers on the topic, we take a top-down approach to 6G. We present a holistic discussion of 6G systems beginning with lifestyle and societal changes driving the need for next generation networks. This is followed by a discussion into the technical requirements needed to enable 6G applications, based on which we dissect key challenges, as well as possibilities for practically realizable system solutions across all layers of the Open Systems Interconnection stack. Since many of the 6G applications will need access to an order-of-magnitude more spectrum, utilization of frequencies between 100 GHz and 1 THz becomes of paramount importance. As such, the 6G eco-system will feature a diverse range of frequency bands, ranging from below 6 GHz up to 1 THz. We comprehensively characterize the limitations that must be overcome to realize working systems in these bands; and provide a unique perspective on the physical, as well as higher layer challenges relating to the design of next generation core networks, new modulation and coding methods, novel multiple access techniques, antenna arrays, wave propagation, radio-frequency transceiver design, as well as real-time signal processing. We rigorously discuss the fundamental changes required in the core networks of the future that serves as a major source of latency for time-sensitive applications. While evaluating the strengths and weaknesses of key 6G technologies, we differentiate what may be achievable over the next decade, relative to what is possible.