Remote sensing image super-resolution (RSISR) is a crucial task in remote sensing image processing, aiming to reconstruct high-resolution (HR) images from their low-resolution (LR) counterparts. Despite the growing number of RSISR methods proposed in recent years, a systematic and comprehensive review of these methods is still lacking. This paper presents a thorough review of RSISR algorithms, covering methodologies, datasets, and evaluation metrics. We provide an in-depth analysis of RSISR methods, categorizing them into supervised, unsupervised, and quality evaluation approaches, to help researchers understand current trends and challenges. Our review also discusses the strengths, limitations, and inherent challenges of these techniques. Notably, our analysis reveals significant limitations in existing methods, particularly in preserving fine-grained textures and geometric structures under large-scale degradation. Based on these findings, we outline future research directions, highlighting the need for domain-specific architectures and robust evaluation protocols to bridge the gap between synthetic and real-world RSISR scenarios.