Prognostic Health Monitoring (PHM) of aerospace engines has a significant impact on predicting the Remaining Useful Life (RUL) of critical components, ensuring operational reliability and timely maintenance. In this study, we investigate Machine Learning and Deep Learning techniques for estimating RUL using the Commercial Modular Aero-Propulsion System Simulation (CMAPSS) dataset provided by NASA. We implemented several models, including traditional regression-based approaches and advanced deep learning architectures, to assess their performance in predicting engine degradation. Among the models tested, the Bidirectional Long Short-Term Memory (Bi-LSTM) network exhibited enhanced predictive accuracy, attaining the minimum Root Mean Square Error (RMSE) and the maximum R-squared (R2) score. Our results indicate that the Bi-LSTM model efficiently captures the temporal dependencies in the sensor data, outperforming other models in providing reliable and early RUL predictions. These results highlight the effectiveness of Bi-LSTM in improving the prognostic capabilities of engine health management systems, contributing to improved safety and maintenance strategies in aerospace applications.