This contributed volume contains articles written by the plenary and invited speakers from the third international MATHEON Workshop 2017 that focus on applications of compressed sensing. This conference will brought together the leading mathematicians working in compressed sensing and the leading engineers from a number of its application areas such as imaging science, radar technology, tomography, or communication theory, to report on recent developments, to promote a dialogue between applied mathematicians and engineers, and to foster new developments and collaborations.  There was also a focus on deep learning, given the expectation of useful interactions between compressed sensing and deep learning.