The notion of categorical model of linear logic is now well studied and established around the notion of linear-non-linear adjunction, which encompasses the previous notions of Seely categories, Lafont categories and linear categories. These categorical structures have counterparts in the realm of ∞-categories, which can thus be thought of as "weak", or "homotopical" models of linear logic. In this talk, we give a tour of categorical semantics of linear logic, and show examples of ∞-categorical models generalizing polynomial functors, generalized species, and models from linear algebra.