Wild animals are under selective pressure to optimise energy budgets; therefore, quantifying energy expenditure, intake and allocation to specific activities is important if we are to understand how animals survive in their environment. One approach toward estimating energy budgets has involved measuring oxygen consumption rates under controlled conditions and constructing allometric relationships across species. However, studying ‘giant’ marine vertebrates (e.g. pelagic sharks, whales) in this way is logistically difficult or impossible. An alternative approach involves the use of increasingly sophisticated electronic tags that have allowed recordings of behaviour, internal states and the surrounding environment of marine animals. This Review outlines how we could study the energy expenditure and intake of free-living ocean giants using this ‘biologging’ technology. There are kinematic, physiological and theoretical approaches for estimating energy expenditure, each of which has merits and limitations. Importantly, tag-derived energy proxies can hardly be validated against oxygen consumption rates for giant species. The proxies are thus qualitative, rather than quantitative, estimates of energy expenditure, and have more limited utilities. Despite this limitation, these proxies allow us to study the energetics of ocean giants in their behavioural context, providing insight into how these animals optimise their energy budgets under natural conditions. We also outline how information on energy intake and foraging behaviour can be gained from tag data. These methods are becoming increasingly important owing to the natural and anthropogenic environmental changes faced by ocean giants that can alter their energy budgets, fitness and, ultimately, population sizes.