In the 19th century, Oscar Wilde stated "We live, I regret to say, in an age of surfaces". Today, we do so even more, and we do not regret it: key advances in the understanding and fabrication of surfaces with controlled wetting properties are about to make the dream of a contamination-free (or 'no-clean') surface come true. Two routes to self-cleaning are emerging, which work by the removal of dirt by either film or droplet flow. Although a detailed understanding of the mechanisms underlying the behaviour of liquids on such surfaces is still a basic research topic, the first commercial products in the household-commodity sector and for applications in biotechnology are coming within reach of the marketplace. This progress report describes the current status of understanding of the underlying mechanisms, the concepts for making such surfaces, and some of their first applications.