I briefly review results obtained within the variational Hamiltonian approach to Yang-Mills theory in Coulomb gauge and confront them with recent lattice data. The variational approach is extended to non-Gaussian wave functionals including three- and four-gluon kernels in the exponential of the vacuum wave functional and used to calculate the three-gluon vertex. A new functional renormalization group flow equation for Hamiltonian Yang--Mills theory in Coulomb gauge is solved for the gluon and ghost propagator under the assumption of ghost dominance. The results are compared to those obtained in the variational approach.
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