Fast dynamics encompasses a range of applications characterised by short time durations, high energy events, and extreme physical phenomena such as impacts, shocks, large deformations, fracture, and fragmentation. These scenarios span diverse fields, including drop tests for handheld devices, car crash simulations, bird impacts on aircraft, ballistic and armour analysis, space debris collisions, and even interplanetary impacts. Despite their variety, these events share commonalities in the underlying physical phenomena, economic significance, and computational challenges. The finite element method (FEM), a widely adopted mesh-based technique, has achieved great success in modelling such problems. However, meshless alternatives have also been successfully explored in cases of extreme deformation, as well as in the simulation of fracture and fragmentation processes. This presentation will explore the use of the meshless Smoothed Particle Hydrodynamics (SPH) method as a competitive alternative to traditional mesh-based approaches for simulating critical phenomena in fast dynamics. The discussion will begin by revisiting the foundational principles of the classic displacement-based SPH formulation [1], highlighting the strengths of meshless techniques while critically addressing the inherent limitations of SPH. Building on this foundation, the talk will transition to a modern approach developed over the past decade, which leverages the discretisation of a system of first-order conservation laws using SPH [2,3]. This methodology not only provides a versatile framework for representing solid dynamics across diverse configurations (e.g., Total Lagrangian and Updated Lagrangian formulations) but also enables the integration of robust numerical stabilisation techniques, many of which have been successfully employed in Computational Fluid Dynamics (CFD). [1] Libersky, L. D., Petschek, A. G., Carney, T. C., Hipp, J. R., Allahdadi, F. A. High strain Lagrangian Hydrodynamics. Journal of Computational Physics (1993) 109:67-75. [2] Hean Lee, C., Gil, A. J., Ghavamian, A., Bonet, J. A Total Lagrangian upwind Smooth Particle Hydrodynamics algorithm for large strain explicit solid dynamics. CMAME (2019) 344:209-250. [3] Refachinho de Campos, P. R., Gil, A. J., Hean Lee, C., Giacomini, M., Bonet, J. A New Updated Reference Lagrangian Smooth Particle Hydrodynamics algorithm for isothermal elasticity and elasto-plasticity CMAME (2022) 392:114680.