Forensic and biometric investigations increasingly depend on surveillance imagery, where low resolution face images must be enhanced without compromising identity information. Face Super Resolution (FSR) addresses this challenge, though balancing perceptual quality with identity consistency under real world conditions proves difficult. However, no prior review jointly analyzes identity-specific metrics, computational efficiency, and forensic deployment constraints. This Systematic Literature Review examines 55 peer reviewed identity preserving FSR methods from 2021 to 2025, spanning CNNs, GANs, Transformers, Diffusion models, Hybrid architectures, Wavelet-based approaches, and emerging techniques. Our analysis reveals distinct optimization strategies rather than a simple trade off. Optimized CNNs like SANet excel in reconstruction fidelity (32.36 dB PSNR on CelebA) while demonstrating strong identity consistency through superior cosine similarity. Conversely, hybrid models like CMANet (CNN-Mamba) prioritize recognition performance with the highest accuracy on SCface (80.58%) and LFW (0.850 AUC) despite lower reconstruction scores (30.31 dB PSNR). Both maintain robust identity preservation but optimize for different criteria SANet for pixel-level fidelity and embedding similarity, CMANet for verification tasks. Three critical gaps limit deployment in forensic contexts: scarce datasets reflecting real surveillance conditions, inconsistent computational efficiency reporting, and hallucination risks threatening reliability in high stakes applications. We propose addressing these through surveillance grade datasets with authentic degradation patterns, standardized evaluation protocols measuring both reconstruction quality and identity preservation performance, and advancing efficient architectures particularly prior guided CNNs and lightweight hybrids suitable for forensic systems requiring accountability. © 2013 IEEE.