In the last decade, Compressed Sensing became an active research area, producing notable speedups in important practical applications. For example, Vasanawala, Lustig and co-workers at Stanford’s Lucille Packard Children’s hospital produced roughly 8X speedups using compressed sensing approaches in the aquisition time of Magnetic Resonance Images, and even larger speedups have been reported in other practical applications, such as Magnetic Resonance spectroscopy. Over the same period, theory in both applied mathematics and information theory developed extremely precise and insightful formulas. However, there are gaps between the two bodies of work, because the rules that practitioners must play by are not always the ones that theorists envision. In this talk, Professor Donoho will survey some recent developments, bringing theory and practice closer together, including multi-scale compressed sensing and cartesian product compressed sensing.