This Review presents a broad overview of adaptations of truly Arctic and Antarctic mammals and birds to the challenges of polar life. The polar environment may be characterized by grisly cold, scarcity of food and darkness in winter, and lush conditions and continuous light in summer. Resident animals cope with these changes by behavioural, physical and physiological means. These include responses aimed at reducing exposure, such as 'balling up', huddling and shelter building; seasonal changes in insulation by fur, plumage and blubber; and circulatory adjustments aimed at preservation of core temperature, to which end the periphery and extremities are cooled to increase insulation. Newborn altricial animals have profound tolerance to hypothermia, but depend on parental care for warmth, whereas precocial mammals are well insulated and respond to cold with non-shivering thermogenesis in brown adipose tissue, and precocial birds shiver to produce heat. Most polar animals prepare themselves for shortness of food during winter by the deposition of large amounts of fat in times of plenty during autumn. These deposits are governed by a sliding set-point for body fatness throughout winter so that they last until the sun reappears in spring. Polar animals are, like most others, primarily active during the light part of the day, but when the sun never sets in summer and darkness prevails during winter, high-latitude animals become intermittently active around the clock, allowing opportunistic feeding at all times. The importance of understanding the needs of the individuals of a species to understand the responses of populations in times of climate change is emphasized.