The regulation and utilization of thermal energy is increasingly important in modern society due to the growing demand for heating and cooling in applications ranging from buildings, to cooling high power electronics, and from personal thermal management to the pursuit of renewable thermal energy technologies. Over billions of years of natural selection, biological organisms have evolved unique mechanisms and delicate structures for efficient and intelligent regulation and utilization of thermal energy. These structures also provide inspiration for developing advanced thermal engineering materials and systems with extraordinary performance. In this review, we summarize research progress in biological and bioinspired thermal energy materials and technologies, including thermal regulation through insulation, radiative cooling, evaporative cooling and camouflage, and conversion and utilization of thermal energy from solar thermal radiation and biological bodies for vapor/electricity generation, temperature/infrared sensing, and communication. Emphasis is placed on introducing bioinspired principles, identifying key bioinspired structures, revealing structure-property-function relationships, and discussing promising and implementable bioinspired strategies. We also present perspectives on current challenges and outlook for future research directions. We anticipate that this review will stimulate further in-depth research in biological and bioinspired thermal energy materials and technologies, and help accelerate the growth of this emerging field.