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The mechanical behaviour of cells is largely controlled by a structure that is fundamentally out of thermodynamic equilibrium: a network of crosslinked filaments subjected to the action of energy-transducing molecular motors. The study of this kind of active system was absent from conventional physics and there was a need for both new theories and new experiments. The field that has emerged in recent years to fill this gap is underpinned by a theory that takes into account the transduction of chemical energy on the molecular scale. This formalism has advanced our understanding of living systems, but it has also had an impact on research in physics per se. Here, we describe this developing field, its relevance to biology, the novelty it conveys to other areas of physics and some of the challenges in store for the future of active gel physics.