Active matter extracts energy from its surroundings at the single particle level and transforms it into mechanical work. Examples include cytoskeleton biopolymers and bacterial suspensions. Here, we review experimental, theoretical and numerical studies of active nematics - a type of active system that is characterised by self-driven units with elongated shape. We focus primarily on microtubule-kinesin mixtures and the hydrodynamic theories that describe their properties. An important theme is active turbulence and the associated motile topological defects. We discuss ways in which active turbulence may be controlled, a pre-requisite to harvesting energy from active materials, and we consider the appearance, and possible implications, of active nematics and topological defects to cellular systems and biological processes.