  Supersymmetric models with t-b-\tau Yukawa unification at M_{GUT}
qualitatively predict a sparticle mass spectrum including first and second
generation scalars at the 3--15 TeV scale, third generation scalars at the
(few) TeV scale and gluinos in the sub-TeV range. The neutralino relic density
in these models typically turns out to lie far above the measured dark matter
abundance, prompting the suggestion that instead dark matter is composed of an
axion/axino mixture. We explore the axion and thermal and non-thermal axino
dark matter abundance in Yukawa-unified SUSY models. We find in this scenario
that {\it i}). rather large values of Peccei-Quinn symmetry breaking scale
f_a\sim 10^{12} GeV are favored and {\it ii}). rather large values of GUT scale
scalar masses \sim 10-15 TeV allow for the re-heat temperature T_R of the
universe to be T_R\agt 10^6 GeV. This allows in turn a solution to the
gravitino/Big Bang Nucleosynthesis problem while also allowing for baryogenesis
via non-thermal leptogenesis. The large scalar masses for Yukawa-unified models
are also favored by data on b\to s\gamma and B_s\to \mu^+\mu^- decay. Testable
consequences from this scenario include a variety of robust LHC signatures, a
possible axion detection at axion search experiments, but null results from
direct and indirect WIMP search experiments.
