This Critical Review reviews the origin and chemical and rheological complexity of radioactive waste at the U.S. Department of Energy Hanford Site. The waste, stored in underground tanks, was generated via three distinct processes over decades of plutonium extraction operations. Although close records were kept of original waste disposition, tank-to-tank transfers and conditions that impede equilibrium complicate our understanding of the chemistry, phase composition, and rheology of the waste. Tank waste slurries comprise particles and aggregates from nano to micro scales, with varying densities, morphologies, heterogeneous compositions, and complicated responses to flow regimes and process conditions. Further, remnant or changing radiation fields may affect the stability and rheology of the waste. These conditions pose challenges for transport through conduits or pipes to treatment plants for vitrification. Additionally, recalcitrant boehmite degrades glass quality and the high aluminum content must be reduced prior to vitrification for the manufacture of waste glass of acceptable durability. However, caustic leaching indicates that boehmite dissolves much more slowly than predicted given surface normalized rates. Existing empirical models based on ex situ experiments and observations generally only describe material balances and have not effectively predicted process performance. Recent advances in the areas of in situ microscopy, aberration-corrected transmission electron microscopy, theoretical modeling across scales, and experimental methods for probing the physics and chemistry at mineral-fluid and mineral-mineral interfaces are being implemented to build robustly predictive physics-based models.