For a finite-dimensional algebra A, being Auslander-Gorenstein is a homological condition which implies many interesting properties for the algebra and for certain subcategories of mod(A). In this talk, we will consider three well-known classes of algebras; namely, gentle, Nakayama, and monomial algebras, and aim to understand what the Auslander-Gorenstein property means in these settings. First, we will try to find a combinatorial characterisation of this homological condition, which leads us to a new class of examples of Auslander-Gorenstein algebras. Second, I will present a surprising new homological characterisation of the Auslander-Gorenstein property for these algebras. For this, a bijection between indecomposable projective and injective A-modules introduced by Auslander and Reiten plays a central role.