Scientists use laboratory experiments to search for molecules with desirable properties, e.g., that make efficient solar cells; or that cure cancer. The success of such a search hinges on making good decisions about which experiments to perform. We show how machine learning and value of information analysis, together in an optimal learning framework, can be used to choose good experiments, and to reach experimental goals reliably with fewer experiments. We first describe how these mathematical methods were used to successfully find minimal peptide substrates for a pair of protein-modifying enzymes. These novel peptides support reversible protein tagging, with application to medicine and biochemical sensors. We then review two other applications: growing carbon nanotubes, and finding peptides that bind to inorganic materials. Peter Frazier received a B.S. in Physics and Engineering/Applied Science from the California Institute of Technology in 2000, after which he spent several years in industry as a software engineer, working for two different start-up companies and for the Teradata division of NCR. In 2005, he entered graduate school in the Department of Operations Research & Financial Engineering at Princeton University, and received an M.A. in 2007 and a Ph.D. in 2009. He joined the faculty at Cornell in 2009 as an Assistant Professor in the School of Operations Research & Information Engineering. His research is in sequential decision-making under uncertainty and optimal methods for collecting information, focusing on applications in simulation and health care. He is the recipient of a CAREER Award from the National Science Foundation and a Young Investigator Award from the Air Force Office of Scientific Research.