  Over the last years the Tevatron Run-II has extended several limits on Higgs
boson masses and coupling which were pioneered during the LEP accelerator
operation between 1989 and 2000. Higgs boson searches will also be at the
forefront of research at the LHC. This review concisely discusses the
experimental constraints set by the CDF and D0 collaborations in winter
2008/2009 at the beginning of the LHC era. Model-independent and
model-dependent limits on Higgs boson masses and couplings have been set and
interpretations are discussed both in the Standard Model and in extended
models. Recently, for the first time the Tevatron excludes a SM Higgs boson
mass range (160-170 GeV) beyond the LEP limit at 95% CL. The experimental
sensitivities are estimated for the completion of the Tevatron programme.
