Higgs searches at the Tevatron

We present combined CDF and D0 searches for the Standard Model (SM) and Minimal Supersymmetric Standard Model (MSSM) Higgs boson using up to 6.7 fb(-1) of integrated luminosity from 1.96 TeV proton-antiproton collisions at the Tevatron. Specialized searches for Higgs bosons produced via gluon fusion, associated boson production, and vector boson fusion, decaying to b (b) over bar, W+ W-, tau(+)tau(-), and gamma gamma are combined to produce 95% CL upper limits on SM Higgs production as a function of mass. Current Tevatron limits are shown, including a new exclusion for SM Higgs masses between 158 and 175 GeV/c(2). We also present prospects for future sensitivity.