  We provide a short review of some aspects of Dark Matter production in non
Standard Cosmology. Considering the simplest Higgs portal model as definite
particle physics setup, we consider the impact on the parameter space
corresponding to the correct relic density, and the complementary experimental
constraints, of the presence, during thermal production, of an exotic component
dominating the energy density of the Universe. In the second part of the work
we will focus on the case that such exotic component satisfies the equation of
state of matter and it can produce DM non-thermally.
