Cosmological horizons play an essential role in determining the causal structure of spacetime and are of central importance in the inflationary universe scenario. We review the topic of horizons in simple language, pointing out a number of widespread misconceptions. The use of spacetime diagrams plotted in terms of proper time and proper distance coordinates helps sort out some of these difficulties. They complement the widely used conformal diagrams, which show causal relations clearly but severely distort proper distances.