Higgs and Coulomb branches of quiver gauge theories form two rich families of Poisson varieties that are expected to be exchanged by 3D mirror symmetry. The Hikita conjectures relate the algebra and geometry of these branches in a nontrivial way, allowing one to extract new structures on one side by studying its mirror. In this talk, I will give an overview of the current state of the Hikita conjecture, with an emphasis on its interplay with the enumerative geometry of the Higgs branch and related combinatorics. I will illustrate how the picture works for ADE quivers.