Research in quasilinear hyperbolic partial differential equations (i.e., “conservation laws”) presents formidable challenges. It is a subject where technical difficulties dominate, and where even the most basic questions (like existence of solutions) have not yet been answered, or have unsatisfactory answers. In this talk, I will try to paint a different picture. In fact, some simple and elegant principles underlie many aspects of the theory, and new and surprising results are always appearing. Barbara Lee Keyfitz is the Dr. Charles Saltzer Professor of Mathematics at The Ohio State University, which she joined in January 2009 after 21 years at the University of Houston and four and a half years as director of the Fields Institute. She received her undergraduate education at the University of Toronto and her M.S. and Ph.D. degrees from the Courant Institute, New York University. Her research area is nonlinear partial differential equations. She has contributed to the study of nonstrictly hyperbolic conservation laws. With Herbert Kranzer, she developed the concept of singular shocks, which occur in some types of systems. With Suncica Canic and others, she was a pioneer in the mathematical theory of self-similar solutions of multidimensional conservation laws. Keyfitz was named fellow of SIAM, AAAS, and AMS, and the recipient of the 2012 SIAM Award for Distinguished Service to the Profession. In 2012, she was the Noether lecturer at the Joint Mathematics Meetings and the Kovalevsky lecturer at the SIAM Annual Meeting. She has received the 2005 Krieger-Nelson Prize of the Canadian Mathematical Society and an honorary Doctor of Mathematics degree from the University of Waterloo. Before joining the faculty of the University of Houston, Keyfitz was a faculty member in engineering at Columbia and Princeton and in mathematics at Arizona State University. She has also held visiting positions at the University of Nice, Duke University, University of California, Berkeley, the IMA, the Fields Institute, and Brown University. She was president of AWM (2005-2006) and currently serves as vice president of AMS and president of the International Council on Industrial and Applied Mathematics.