Rubber extrusion has evolved through overlapping advances in equip design, rheological characterization, numerical modeling, sensing, and control. This structured critical narrative review synthesizes 180 sources published from 1972 to 2026, assembled through iterative keyword searching and backward and forward citation tracing. The conventional three-zone theory of solid conveying, compression, and metering is used as a bounded analytical framework, while the literature is organized into four overlapping analytical periods spanning empirical design, constitutive and numerical modeling, engineering-scale simulation, and multiphysics and data-enabled methods. Evidence is distinguished among direct rubber-extrusion validation, rubber-material or rheological studies, transferable general polymer extrusion studies, and enabling computational, sensing, or control research. Five persistent challenges are identified: formulation-dependent nonlinear rheology; incomplete representation of filler-network evolution and wall slip; limited cross-machine and cross-formulation validation; high computational cost; and the lack of standardized datasets and reporting protocols. Digital twins, physics-informed neural networks, and neural operators are promising but remain insufficiently validated for industrial rubber extrusion. Priorities include transparent benchmark datasets, evidence-graded, uncertainty- and latency-aware validation, multimodal sensing, transferable reduced-order and learned models, and measurable sustainability indicators. Together, these priorities define a validation-oriented roadmap for more reliable, transferable, and sustainable rubber-extrusion modeling and control.