  Recent results obtained for the deconfinement phase transition within the
Hamiltonian approach to Yang-Mills theory are reviewed. Assuming a
quasiparticle picture for the grand canonical gluon ensemble the thermal
equilibrium state is found by minimizing the free energy with respect to the
quasi-gluon energy. The deconfinement phase transition is accompanied by a
drastic change of the infrared exponents of the ghost and gluon propagators.
Above the phase transition the ghost form factor remains infrared divergent but
its infrared exponent is approximately halved. The gluon energy being infrared
divergent in the confined phase becomes infrared finite in the deconfined
phase. Furthermore, the effective potential of the order parameter for
confinement is calculated for SU$(N)$ Yang-Mills theory in the Hamiltonian
approach by compactifying one spatial dimension and using a background gauge
fixing. In the simplest truncation, neglecting the ghost and using the
ultraviolet form of the gluon energy, we recover the Weiss potential. From the
full non-perturbative potential (with the ghost included) we extract a critical
temperature of the deconfinement phase transition of $269$ MeV for the gauge
group SU$(2)$ and $283$ MeV for SU$(3)$.
