Feature matching is a challenging computer vision task that involves findingcorrespondences between two images of a 3D scene. In this paper we consider thedense approach instead of the more common sparse paradigm, thus striving tofind all correspondences. Perhaps counter-intuitively, dense methods havepreviously shown inferior performance to their sparse and semi-sparsecounterparts for estimation of two-view geometry. This changes with our noveldense method, which outperforms both dense and sparse methods on geometryestimation. The novelty is threefold: First, we propose a kernel regressionglobal matcher. Secondly, we propose warp refinement through stacked featuremaps and depthwise convolution kernels. Thirdly, we propose learning denseconfidence through consistent depth and a balanced sampling approach for denseconfidence maps. Through extensive experiments we confirm that our proposeddense method, \textbf{D}ense \textbf{K}ernelized Feature \textbf{M}atching,sets a new state-of-the-art on multiple geometry estimation benchmarks. Inparticular, we achieve an improvement on MegaDepth-1500 of +4.9 and +8.9AUC$@5^{\circ}$@5∘ compared to the best previous sparse method and dense methodrespectively. Our code is provided at https://github.com/Parskatt/dkm