Damage and fracture modeling in materials and structures remains a complex challenge due to the highly nonlinear mechanisms involved. Phenomena such as strain-softening behavior, the loss of ellipticity in governing equations, and localization effects significantly complicate the search for an objective solution to the mechanical problem. Although various conventional and advanced numerical approaches have been developed, researchers continue to focus extensively on these issues to devise efficient strategies for accurately capturing the initiation and evolution of damage in traditional and innovative materials. This minisymposium is dedicated to exploring recent developments in computational methods, with a particular emphasis on simulating damage and fracture processes. We invite contributions on topics including, but not limited to advanced discretization strategies for phase-field fracture modelling; enriched finite element techniques; virtual element methods for simulating crack propagation; eigenerosion and eigenfracture approaches; enhanced cohesive zone models; meshfree techniques for fracture analysis, peridynamics-based fracture modelling.