  I report on recent results obtained within the Hamiltonian approach to QCD in
Coulomb gauge. Furthermore this approach is compared to recent lattice data,
which were obtained by an alternative gauge fixing method and which show an
improved agreement with the continuum results. By relating the Gribov
confinement scenario to the center vortex picture of confinement it is shown
that the Coulomb string tension is tied to the spatial string tension. For the
quark sector a vacuum wave functional is used which explicitly contains the
coupling of the quarks to the transverse gluons and which results in
variational equations which are free of ultraviolet divergences. The
variational approach is extended to finite temperatures by compactifying a
spatial dimension. The effective potential of the Polyakov loop is evaluated
from the zero-temperature variational solution. For pure Yang--Mills theory,
the deconfinement phase transition is found to be second order for SU(2) and
first order for SU(3), in agreement with the lattice results. The corresponding
critical temperatures are found to be $275 \, \mathrm{MeV}$ and $280 \,
\mathrm{MeV}$, respectively. When quarks are included, the deconfinement
transition turns into a cross-over. From the dual and chiral quark condensate
one finds pseudo-critical temperatures of $198 \, \mathrm{MeV}$ and $170 \,
\mathrm{MeV}$, respectively, for the deconfinement and chiral transition.
