Peak power control for multicarrier communications has been a long-lasting problem in signal processing and communications. However, industry and academia are confronted with new challenges regarding energy efficient system design. Particularly, the envisioned boost in network energy efficiency (e.g. at least by a factor of 1000 in the Green Touch consortium) will tighten the requirements on component level so that the efficiency gap with respect to single-carrier transmission must considerably diminish. This paper reflects these challenges together with a unified framework and new directions in this field. The combination of large deviation theory, de-randomization and selected elements of Banach space geometry will offer a novel approach and will provide ideas and concepts for researchers with a background in industry as well as those from academia.