Applied mathematics is also concerned with the manipulation and analysis of signals and data. In our digital world, where huge amounts of data are routinely collected, transmitted, processed, analysed, compressed, encrypted, decrypted, and stored, efficient mathematical methods and numerical algorithms are needed. ‘Can you picture that? X-rays, DNA, and photos’ outlines how applied mathematics is used to extract information from this data using the examples of computed tomography, X-ray crystallography, and the compression of digital image files. Modern developments have seen the discovery of new methods to extract information and process it efficiently. Examples are the theory of wavelets and compressed sensing, which has been implemented in Magnetic Resonance Imaging scanners.