Climate change mitigation scenarios that meet the Paris Agreement's objective of limiting global warming usually assume an important role for carbon dioxide removal and negative emissions technologies. Direct air capture (DAC) is a carbon dioxide removal technology which separates CO2 directly from the air using an engineered system. DAC can therefore be used alongside other negative emissions technologies, in principle, to mitigate CO2 emissions from a wide variety of sources, including those that are mobile and dispersed. The ultimate fate of the CO2, whether it is stored, reused, or utilised, along with choices related to the energy and materials inputs for a DAC process, dictates whether or not the overall process results in negative emissions. In recent years, DAC has undergone significant technical development, with commercial entities now operating in the market and prospects for significant upscale. Here we review the state-of-the-art to provide clear research challenges across the process technology, techno-economic and socio-political domains.