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**Abstract.** I will overview recent advances on nonlinear wave phenomena with singularities. Interfaces and shock waves are important in fluid dynamics, material dynamics, astrophysics, cosmology, etc. On the one hand, propagating interfaces arise in solid materials undergoing phase transitions of martensite-austenite type. On the other hand, at the other end of the scale spectrum, the first observation of gravitational waves in our Universe was made in Sept. 2015 (and announced in Feb. 2016), and solutions to the Einstein equations may also exhibit gravitational singularities. In these fields of research, the problems posed to applied mathematicians are multi-fold and, often, involve several scales and complex interactions of nonlinear waves. Making advances in the physical modeling, mathematical analysis, and scientific computation requires to unify many different techniques. Research in these directions has led to exciting mathematical and numerical developments on the Euler equations and the Einstein equations. Blog: philippelefloch.org

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