Time-varying data is generated or measured in domains as diverse as computational fluid dynamics, hurricanes and so on. The data generally contains specific features as well as events that are of interest to an application expert. We present novel art-inspired techniques for visualizing time-varying data that conveys change over time in a single image. Illustrators and painters have conveyed concepts such as motion and other change over time using illustrative cues. Time-varying data in which three-dimensional features are moving over time, can be effectively visualized using our illustrative techniques such as speedlines, flow ribbons, strobe silhouettes and opacity-based techniques. We applied these techniques to computational fluid dynamics data as well as hurricanes. Our illustration-inspired techniques allowed our collaborators to obtain further insight into the evolution and intensification of a hurricane. For effectively visualizing time-varying data such as infant mortality, global rainfall, voting patterns over time, we developed a novel pointillism-based technique inspired by Seurat. These techniques convey variability as well as trends over time in a single image.