Instances of Higher Geometry in Field Theory

Generalisations of geometry have emerged in various forms in the study of field theory and quantization. This mini-review focuses on the role of higher geometry in three selected physical applications. After motivating and describing some basic aspects of algebroid structures on bundles and (differential graded) Q-manifolds, we briefly discuss their relation to ($\alpha$) the Batalin-Vilkovisky quantization of topological sigma models, ($\beta$) higher gauge theories and generalized global symmetries and ($\gamma$) tensor gauge theories, where the universality of their form and properties in terms of graded geometry is highlighted.