This review consolidates decades of research on hot-deformation processing maps into a single, mechanism-based framework that connects macroscopic stability criteria with high-temperature deformation physics. It traces the evolution of major formulations—including those by Prasad, Murty, and Kim–Jeong—back to their common thermokinetic foundation in creep and dynamic-recrystallization (DRX) kinetics. Through this unified treatment, the review clarifies that power-dissipation efficiency (η) and flow-instability indices are different projections of the same rate-dependent constitutive response, which also dictates transitions between power-law deformation mechanism regimes and the onset of power-law breakdown. The paper is organized to move from theory to application. Early sections reconstruct the mathematical origin and physical meaning of η and instability functions; middle sections benchmark these criteria across published Mg datasets; and later sections provide practical guidance for constructing reliable maps using physics-constrained regression and uncertainty reporting. The review further clarifies—by distinguishing necessity from sufficiency in the DRX–η relationship—why DRX annotations and high-η domains frequently coincide without implying causal equivalence. Collectively, these contributions transform processing maps from empirical contour charts into predictive diagnostic tools and offers a reproducible workflow and interpretive hierarchy adaptable to diverse alloy systems and data qualities.