Geometric models, originating in triangulations of surfaces in cluster theory in the early 2000s, provide powerful tools for the structural understanding of categories by permitting the use of combinatorial and topological methods. They have highlighted unexpected applications and connections between different branches of mathematics, such as representation theory, symplectic geometry and theoretical physics. Although gentle algebras are derived-tame, natural generalisations of gentle algebras, such as string and special biserial algebras, are no longer derived-tame. But their module categories are tame. In this talk I will illustrate, via examples, how the combinatorics of these classes of algebras can be understood via geometric models and give some applications of geometric models in representation theory.