<p>Inter and intra-site correlation of ground-motion intensity measures (IMs) plays a critical role in seismic hazard and risk assessment. Ignoring such correlations can lead to significant misrepresentation of losses in regional-scale studies and misrepresentation of ground motion field simulations. Accurate correlation modelling is essential for scenario-based risk assessments, emergency preparedness planning, and understanding systematic infrastructure vulnerabilities in portfolio risk analyses. This study presents a detailed overview of intra-site (non-spatial) and inter-site (spatial) correlation models developed over the past two decades. It reviews over 45 models proposed in the literature, encompassing diverse methodologies applied to different regional databases and a variety of IM. The analyses reveal considerable variability among models, particularly in short-range spatial correlation and in how inter-IM correlations are treated. Despite this diversity, most models rely on simplifying assumptions such as stationarity and isotropy, which may not fully capture the complexities of real-world ground motion patterns. This work provides a valuable resource for researchers and practitioners by summarising the current state of correlation modelling and offering guidance on model selection based on database, regional context, and engineering application. It underscores the importance of informed model choice for improving the accuracy of hazard and risk assessments in spatially distributed systems.</p>