A new generation of extreme matter experiments is underway, recreating conditions that exist deep inside stars, sub-stellar objects (e.g., brown dwarfs), and planets, and creating materials not previously imagined. Exquisite pressure control with modern laser or pulsed power drivers can now produce new quantum states of matter with atoms brought together closer than the Bohr radius, where core electron chemistry is plausible. I will show the first structural and mechanical data for solids at TPa (1 TPa = 10 million atmospheres) conditions and describe how these data provide compositional insight for solar and extrasolar planets and new constraints for quantum-many-body theory. At higher temperatures, dense plasma data for several materials reveal new chemically-rich phases well into the multi-TPa regime. The European XFEL offers the transformational next step for exploring this extreme matter frontier, providing an essential guide for first principles theory and changing the way we think about planets, (platforms for life throughout the universe), stars and potential new materials.