  Motivated by Higgs Portal and Hidden Valley models, heavy particle dark
matter that communicates with the supersymmetric Standard Model via pure Higgs
sector interactions is considered. We show that a thermal relic abundance
consistent with the measured density of dark matter is possible for masses up
to $\sim 30\tev$. For dark matter masses above $\sim 1\tev$, non-perturbative
Sommerfeld corrections to the annihilation rate are large, and have the
potential to greatly affect indirect detection signals. For large dark matter
masses, the Higgs-dark-matter-sector couplings are large and we show how such
models may be given a UV completion within the context of so-called "Fat-Higgs"
models. Higgs Portal dark matter provides an example of an attractive
alternative to conventional MSSM neutralino dark matter that may evade
discovery at the LHC, while still being within the reach of current and
upcoming indirect detection experiments.
