This symposium focuses on the latest developments regarding space-time methods for numerical simulation and modelling in engineering. These methods have gained interest in recent years with works exploring different aspects and new concepts. These recent works explore the mathematical aspects (from the numerical analysis point of view), the formulation of space-time problems (with Hamiltonian-like approaches), discretisation technics (continuous vs discontinuous Galerkin, IGA, VEM…), and numerical aspects (mesh refinement, domain decomposition, space-time integration, matrix-free approaches…). Such topics are the most representative examples of the recent literature. Some of the advantages of Space-Time approaches over more classical ones are well known: they open the door to space-time parallelization or space-time adaptivity, they enable to deal with global optimisation or inverse problems in a more direct manner, h- and p- convergence in space and time can be shown to be optimal at least for simple problems, etc. In addition, they can also open up new possibilities for multiphysics and non-linear problems for instance dealing with different time scales in a space-time multi-grid approach just by playing with the different grid sizes or with the approximation functions. The topics covered by this MS include (but are not limited to): • Mathematical aspect of space-time methods; • Space-time discretization technics; • Space-time parallelization and numerical performance; • Space-time for multiphysics and/or non-linear problems; • Space-time for structural problems; • Numerical and algorithmic aspects.