Research is of little use if its results are not effectively communicated. Data visualised in graphs (and tables) are key components in any scientific report, but their design leaves much to be desired. This viewpoint focuses on graph design, following two general principles: clear vision and clear understanding. Clear vision is achieved by maximising the signal to noise ratio. In a graph, the signal is the data in the form of symbols, lines or other graphic elements, and the noise is the support structure necessary to interpret the data. Clear understanding is achieved when the story in the data is told effectively, through organisation of the data and use of text. These principles are illustrated by original and improved graphs from recent publications, completed by tutorial material online (appendices, web pages and film clips). The popular matrix form (multiple graphs in one frame) is discussed as a special case. Differences between publication (including the proofing stage) and presentation are outlined. Suggestions are made for better peer review and processing of graphs in the publication stage.