Market instability and risk broadcast are critical trepidations in economics, predominantly in the background of increasing global financial incorporation and recurrent economic shocks. Accurate modeling of these undercurrents is vital for representatives, investors, and managers to mitigate systemic risks and prediction the effects of contamination. This review aims to systematically examine the evolution, application, and comparative performance of econometric methods used in analyzing market volatility and inter-market risk transmission. It identifies main methodologies, tourist attractions their strengths and limitations, and appraises their suitability under different financial conditions. A comprehensive poetry search was showed using databases such as Scopus, and Web of Science, focusing on peer-reviewed studies available between 2015 and 2025. Selected papers were analyzed based on criteria including organizational rigor, data sources, model robustness, and real-world applicability. The review also employs forest plots to visually summarize the magnitude and direction of volatility spillovers and indecision transmission across marketplaces. The review divulges that while traditional models remain foundational, newer approaches such as Markov-switching regimes, wavelet based techniques, and Machine Learning (ML) hybrids offer improved forecasting performance and adaptability to nonlinear market behavior. The findings suggest a shift toward more dynamic and data intensive econometric tools that better accommodate structural breaks, non-stationarities, and asymmetric shocks. The review concludes by highlighting the significance of combining economic theory with advanced statistical and computational methods to improve the predictive accuracy and practical relevance of volatility and risk transmission models in a progressively complex global financial landscape.