Proximity operators were introduced by Jean Jacques Moreau in 1962 in connection
with problems in unilateral mechanics. They have recently become prominent tools in
the modeling and the numerical solution of problems in data science. In this talk, an
overview of proximity operators will be provided as well as recent developments in the
area of complex structured optimization problems. Applications to machine learning, inverse
problems, and image recovery will be discussed. Open conjectures and mathematical
challenges in the field will also be presented.