Wind spectrum models are pivotal in various fields, ranging from structural engineering to meteorology. This review meticulously examines the origination, development, and applications of five prominent theoretical models of wind spectra. Each model is scrutinised for its analytical expressions and underlying assumptions, providing a comprehensive understanding of their evolution over time. The journey commences with a historical overview, tracing the inception of these models and the seminal contributions that shaped their formulation. Subsequently, the development trajectory of each model is delineated, highlighting key advancements and refinements made in response to empirical observations and theoretical insights. In order to assess the practical efficacy of these models, real-field data has been subjected to spectral analysis using both Welch and FFT methods. Through rigorous comparative analysis, the performance of each spectrum model has been evaluated in terms of its ability to capture the complex dynamics of wind behaviour across different spatial and temporal scales. Moreover, this research highlights the evolution of wind spectrum modelling by elucidating the field's contemporary trends and emerging paradigms. Insights gleaned from this analysis deepen our understanding of atmospheric dynamics and inform the development of more robust and accurate wind spectrum models for diverse engineering and environmental applications. This review is a comprehensive compendium of wind spectrum models, offering invaluable insights into their historical development, theoretical underpinnings, practical applicability, and future prospects.