Falls represent a significant health risk, particularly among older adults and individuals with mobility impairments, and are a leading cause of severe injuries and costly hospitalizations. Fall detection systems have emerged as a critical solution by providing rapid detection and alert mechanisms to mitigate these risks. However, challenges such as high false positives and negatives, limited diverse datasets, privacy concerns, lack of personalization, and reduced robustness in complex environments persist. This chapter provides a comprehensive examination of fall detection algorithms, tracing their evolution from threshold-based methods to advanced machine learning and deep learning models. It explores the underlying principles of these algorithms, focusing on their reliance on wearable sensors, ambient sensors, and computer vision to accurately identify falls in various environments. Key performance metrics like accuracy, sensitivity, specificity, and real-time responsiveness are evaluated, alongside implementation challenges such as sensor fusion, data privacy, and energy efficiency. By presenting current advancements and challenges, this chapter aims to guide researchers in developing context-aware, personalized fall detection systems that leverage multi-modal sensor data and advanced AI/ML techniques to address these critical issues.