Meso-scale structures, such as core-periphery (CP) and community structure, have attracted significant attention in modern network science. While communities are characterized by dense intra-group and sparse inter-group connections, CP structures consist of a densely interconnected core and a loosely connected periphery, where peripheral nodes are typically linked to the core. Despite growing interest, identifying CP structures remains an ill-posed problem, with no universally accepted definition or standardized detection methodology. This ambiguity has led to conceptual overlaps, inconsistent evaluation metrics and slowed methodological progress. In this review, we provide a structured overview of foundational concepts, recent advances, key challenges and comparative evaluations of CP detection approaches, along with a discussion of their interplay with community structure and applications in real-world networks.