  We briefly review several Higgs inflation models and discuss their
cosmological implications. We first classify the inflation models according to
the predicted value of the tensor-to-scalar ratio: (i) $r = {\cal
O}(0.01-0.1)$, (ii) $r = {\cal O}(10^{-3})$, and (iii) $r \ll 10^{-3}$. For
each case we study (i) the Higgs inflation with a running kinetic term, (ii)
the Higgs inflation with a non-minimal coupling to gravity, and (iii) the $B-L$
Higgs inflation. In the last case we introduce supersymmetry to suppress the
Coleman-Weinberg corrections for successful inflation, and derive the upper
bound on the SUSY breaking scale. Interestingly, the SUSY $B-L$ Higgs inflation
requires the SUSY breaking scale of order ${\cal O}(100)$\,TeV to explain the
observed spectral index. We briefly discuss a topological Higgs inflation which
explains the origin of the standard model near-criticality. We also mention the
possibility of Higgs domain walls and the gravitational waves emitted by the
collapsing domain walls.
