Ammonia is an important nutrient for the growth of plants. In industry, ammonia is produced by the energy expensive Haber-Bosch process where dihydrogen and dinitrogen form ammonia at a very high pressure and temperature. In principle one could also reduce dinitrogen upon addition of protons and electrons similar to the mechanism of ammonia production by nitrogenases. Recently, major breakthroughs have taken place in our understanding of biological fixation of dinitrogen, of molecular model systems that can reduce dinitrogen, and in the electrochemical reduction of dinitrogen at heterogeneous surfaces. Yet for efficient reduction of dinitrogen with protons and electrons major hurdles still have to be overcome. In this tutorial review we give an overview of the different catalytic systems, highlight the recent breakthroughs, pinpoint common grounds and discuss the bottlenecks and challenges in catalytic reduction of dinitrogen.