  The recent observation at the Tevatron of $\Sigma_b^{\pm}$ ($uub$ and $ddb$)
baryons within 2 MeV of the predicted $\Sigma_b - \Lambda_b$ splitting and of
$\Xi_b^-$ $(dsb)$ baryons at the Tevatron within a few MeV of predictions has
provided strong confirmation for a theoretical approach based on modeling the
color hyperfine interaction. The prediction of $M(\Xi^-_b) = 5790$ to 5800 MeV
is reviewed and similar methods used to predict the masses of the excited
states $\Xi_b^\prime$ and $\Xi_b^*$. The main source of uncertainty is the
method used to estimate the mass difference $m_b - m_c$ from known hadrons. We
verify that corrections due to the details of the interquark potential and to
$\Xi_b$--$\Xi_b^\prime$ mixing are small. For S-wave $qqb$ states we predict
$M(\Omega_b) = 6052.1 \pm 5.6$ MeV, $M(\Omega^*_b) = 6082.8 \pm 5.6$ MeV, and
$M(\Xi_b^0) = 5786.7 \pm 3.0$ MeV. For states with one unit of orbital angular
momentum between the $b$ quark and the two light quarks we predict
$M(\Lambda_{b[1/2]}) = 5929 \pm 2$ MeV, $M(\Lambda_{b[3/2]}) = 5940 \pm 2$ MeV,
$M(\Xi_{b[1/2]}) = 6106 \pm 4$ MeV, and $M(\Xi_{b[3/2]}) = 6115 \pm 4$ MeV.
Results are compared with those of other recent approaches.
