The importance of graphical displays in statistical practice has been recognized sporadically in the statistical literature over the past century, with wider awareness following Tukey’s Exploratory Data Analysis (1977) and Tufte’s books in the succeeding decades. But statistical graphics still occupies an awkward in-between position: Within statistics, exploratory and graphical methods represent a minor subfield and are not wellintegrated with larger themes of modeling and inference. Outside of statistics, infographics (also called information visualization or Infovis) is huge, but their purveyors and enthusiasts appear largely to be uninterested in statistical principles. We present here a set of goals for graphical displays discussed primarily from the statistical point of view and discuss some inherent contradictions in these goals that may be impeding communication between the fields of statistics and Infovis. One of our constructive suggestions, to Infovis practitioners and statisticians alike, is to try not to cram into a single graph what can be better displayed in two or more. We recognize that we offer only one perspective and intend this article to be a starting point for a wide-ranging discussion among graphics designers, statisticians, and users of statistical methods. The purpose of this article is not to criticize but to explore the different goals that lead researchers in different fields to value different aspects of data visualization. Infovis and Statistical Graphics: Different Goals, Different Looks