Detailed understanding of the equation of state of light elements such as the hydrogen isotopes in the warm dense matter (WDM) regime is essential for the modeling of the inner structure of many astrophysical objects, in particular Jovian planets as well as inertial confinement fusion (ICF) research. In these systems quantum degeneracy and strong inter-particle forces play an important role making its theoretical description extremely challenging. The Omega laser was used to drive a planar shock wave in cryogenically cooled deuterium creating WDM conditions. We used a set of independent diagnostics to measure the thermodynamic conditions of WDM including velocity interferometry (VISAR), streaked optical pyrometry (SOP) and x-ray Thomson scattering (XRTS). With a narrow-band x-ray backlighter probe at backscattering geometry the spectrally resolved XRTS accessed the boundary of collective and non-collective regimes making our measurement sensitive to both electron temperature and density. This work presents a full set of measurements of the thermodynamic properties for different laser intensity drives creating warm dense deuterium at various degrees of degeneracy and coupling. The measured electron densities and temperatures ranged between 0.2 and 2.15x10²³ cm^−3 and 0.6 − 20 eV respectively. The scattering measurement confirmed the findings from the VISAR and SOP data and together densityfunctional molecular dynamics (DFT-MD) simulations provides a novel self-consistent approach for an accurate characterization of the microscopic structure of WDM. Complementary to the laser compression work, findings from project employing static compression hydrogen with the use of diamond anvil cells is also be presented. The first direct measurement of the local field correction to the Coulomb interactions in degenerate plasma was obtained from inelastic scattering (20 keV probe) at the Diamond Light Source synchrotron facility.