This meeting will focus on recent applications of non-archimedean geometry and logarithmic geometry to the study of singularities. Those theories appear to be very adapted to the study of families of singularities, and in particular to approach equisingularity problems, phenomena related to mirror symmetry, degenerations and monodromy of Milnor fibrations, and Lipschitz geometry; they can also provide a unifying framework that brings together other tools often deployed in singularity theory, such as resolution of singularities, tropical geometry, arc spaces, motivic integration, and the minimal model program. There will be three mini-courses, each 3 hours long, and several fifty minutes long research talks.  This meeting is also an activity of the ANR SINTROP.