This work presents the main implications of simultaneously considering the Peccei-Quinn solution

to the Strong CP Problem and the supersymmetric solution to the Hierarchy Problem. We focus our

discussion on the cosmological consequences of the resulting low energy effective theory,

the Minimal Supersymmetric Standard Model augmented with the axion supermultiplet or PQMSSM.

Here we review the main ideas and concepts necessary for discussing the PQMSSM cosmology and

apply these to particular PQMSSM scenarios, such as the axino LSP and the neutralino LSP cases.

In particular we discuss how these scenarios can be made consistent with cosmological constraints,

such as the observed Dark Matter relic density and Big Bang nucleosynthesis.

The implications for collider and dark matter experiments are also presented.