Explore a concise yet comprehensive overview of compressed sensing and its applications in engineering applied mathematics. Gain insights into the context of sparsity and compression, learn practical rules of thumb, and discover key ingredients for applying compressed sensing effectively. Delve into topics such as compression versus compressed sensing, pixel space, reconstruction techniques, beating Shannon-Nyquist theorem, robust statistics, outlier rejection, L1 minimization, and the promotion of sparsity. Understand why compressed sensing is not limited to image processing and explore its broader applications in various fields.