The methods emerging from the field of computational topology are gaining increasing relevance in various aspects of materials science. Examples include porous media flow, flow through membranes, network-based transport, dense suspensions, and granular matter, among others. Topology-based methods correlate structure and performance, help explain and understand experimental and computational results, and propose new materials with superior properties for the applications considered. We envision an interdisciplinary mini-symposium involving materials scientists and engineers, mathematicians focusing on various applied aspects of computational topology, computational scientists developing new numerical methods, data scientists analyzing various aspects of data from experiments and simulations, and machine learning and AI developers, who may find the data emerging from computational topology-based approaches useful for developing novel methods.