Abstract: Haskell, Hrushovski and Macpherson developed the theory of stable domination: a notion that captures when a structure is controlled by its stable part. A prime example is ACVF, where the stable part coincides with all the sets that are internal to the residue field (which is strongly minimal). In this talk we present residue field domination statements for henselian valued fields of equicharacteristic zero, which in essence captures the notion that the structure is controlled by the sorts internal to the residue field. If time allows us, we present residue domination results for sigma-henselian valued fields (this is joint work with D. Haskell).