Kahler Gradient Ricci Solitons (KGRS) are fundamental in the study of Ricci flows on complex manifolds. It has mutually compatible structures: an almost complex structure, a symplectic form, a Riemannian metric, and a potential function all defined on a differentiable manifold. Thus, it is a great playground for many theories to meet and interact: from contact structures, isoparametric functions to symplectic geometry and Morse functions. In this talk, we'll review a few examples and discuss how much and how little symmetry a KGRS could admit. The former is relatively easy while the latter is more challenging. The focus will be on real dimension four where there have been significant recent developments.