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Aschbacher announced a program to revisit the classification of finite simple groups via fusion systems. For that purpose, he developed a local theory of fusion systems in analogy to the local theory of finite groups. Chermak introduced localities, which are group-like algebraic structures associated to fusion systems. We outline how one can revisit and extend the local theory of fusion systems via a local theory of localities, and we indicate how one might be able to overcome some of the technical problems in Aschbacherâ s program by working with localities rather than with fusion systems. The first part of this work is joint with Chermak, the second part is joint with Grazian.