Abstract: Technological advances are often accompanied by significant developments in materials science. Advanced manufacturing techniques for, and discovery of, new materials or properties is a time, cost, and labor involved process. In this talk, I will highlight several places where topological frameworks have been used to support and understand multiple facets of materials science. Among these topics will be the use of persistent homology in machine learning tasks, fiber bundles to explore many-to-one mappings in manufacturing, and Haldane bundles in topological materials. This talk is intended to provide a broad view of the flexibility of topology in a domain science and encourage follow-on discussions regarding specific problems.