Rayleigh-Taylor (RT) instability develops at the interface between two fluids of different densities accelerated against their density gradients. Intense interfacial fluid mixing ensues with time. RT mixing controls a broad range of processes in fluids, plasmas, materials, at astrophysical and at molecular scales. In this work we focus on the physics of RT mixing, which we have identified through our theoretical and experimental studies. The theory analyzes symmetries and invariants of RT dynamics and finds that RT mixing has strong correlations, weak fluctuations, and is sensitive to deterministic conditions. The experiment unambiguously observes heterogeneity, anisotropy and sensitivity to deterministic conditions of RT mixing in a broad range of setups. The theory and the experiment agree with one another, reveal that RT mixing may exhibit order and suggest new avenue for studies interfacial mixing in nature and technology.