A complete Kähler metric \(g\) on a Kähler manifold \(M\) is a "gradient Kähler-Ricci soliton" if there exists a smooth real-valued function \(f : M \to \mathbb{R}\)  with \(\nabla f\) holomorphic such that \(Ric(g)-Hess(f)+\lambda g=0\)  for \(\lambda\) a real number. I will present some classification results for such manifolds. This is joint work with Alix Deruelle (Université Paris-Sud) and Song Sun (UC Berkeley).