Algebraic geometry is not the only traditional form of geometry which may be understood in terms of stability theory. Indeed, compact analytic geometry, differential algebraic geometry, and difference and positive characteristic variants of these all fit into this framework.

General theorems from geometric stability theory apply to these geometric structures and, as such, are meaningful geometrically. For example, the trichotomy theorem interpreted in these geometries exposes the possible basic geometries and has been used to prove finteness theorems in diophantine geometry. In another direction, binding groups in stable theories specialize to give a general theory of differential Galois groups and some structure theorems for compact complex manifolds.

Since compact complex manifolds and differential varieties come from geometry, proofs of geometric properties of these structures based on combnatorial geometries are necessarily indirect. In fact, some of the model theoretic analysis may be performed by the native geometries.

While the theorems of Morley and Baldwin-Lachlan and the notable applications of geometric stability theory to geometry concern structures of finite rank, the bulk of the work on classification theory deals with structures of potentially infinite rank. In these theories the rôle of strongly minimal sets is played by regular types. The infinite rank theory may be used to show that the geometric complexity of general PDEs may be reduced to that of linear PDEs, but it is conceivable that the very same reduction may teach us about how complicated forking in ℵ₀-stable theories can be. These new geometric vistas may prove the truth of Zilber's vision of the reality of geometric model theory.