Hot-melt pressure-sensitive adhesives (HMPSAs) represent a solvent-free adhesive technology that integrates the rapid solidification of hot-melt adhesives with the viscoelastic tack and removability of pressure-sensitive adhesives. While conventional HMPSAs offer advantages such as high-speed processability and low volatile organic compound emissions, growing regulatory and environmental pressures necessitate the development of sustainable and eco-friendly alternatives. This review critically examines polymer design strategies for HMPSAs with emphasis on bio-based polymers, renewable tackifiers, viscoelastic optimization, and recyclability-oriented formulation approaches. Quantitative structure–property relationships involving glass transition temperature, melt viscosity, peel and shear strength, and rheological moduli are discussed to highlight performance–sustainability trade-offs. Advanced characterization techniques, including probe tack testing, shear adhesion failure temperature analysis, time–temperature superposition, and atomic force microscopy, are reviewed to elucidate interfacial and bulk adhesion mechanisms. End-of-life challenges such as adhesive residue during paper and plastic recycling are addressed, alongside emerging solutions including clean-removal and debond-on-demand HMPSAs. The review provides a comprehensive framework for designing next-generation sustainable HMPSAs that balance performance, processability, and environmental responsibility.