This study presents a narrative review of semi-parametric survival analysis applications in economics and finance from 2019 to 2024, analyzing trends and methodological implementations. Through a targeted search of Scopus and Web of Science databases, we identified and examined 73 relevant articles. The analysis reveals that the Cox proportional hazards model predominates (34 studies), particularly valued for its flexibility with censored data and effectiveness in modeling event risks like bankruptcies, firm survival, and credit defaults. The review uncovers consistent geographic and sectoral patterns, with economic conditions, innovation, and managerial factors emerging as critical determinants of business longevity. While demonstrating the method's robustness, we identify limitations in capturing nonlinear relationships and propose integrating advanced techniques to enhance future applications. These findings position semi-parametric survival analysis as a versatile analytical framework, while highlighting pathways for methodological innovation in economic and financial research.