This paper reviews the many ways curves are used to encode data in information visualization. As part of our review, we introduce a curve-based visualization framework where data can be encoded in two major ways: i) through a curve’s shape (a process we call embedding) and ii) through a curve’s local visual attributes (a process we call enrichment). Our framework helps describing and organizing the rich design space of curve-based data visualizations, and offer inspiration for novel data visualizations.