Over the past years, Fall Detection System (FDS) has undergone extensive research to improve living risk, especially for the elderly who are vulnerable to these fall events. Devices employing sensors are crucial components of FDS in achieving high accuracy and sensitivity. This article overviews different sensor modalities, such as ambient-based and vision-based systems, as well as commonly used wearable devices for fall detection, along with the associated data processing algorithms. The critical elements of fall detection, such as architectures and algorithms for processing sensor data, machine learning and deep learning methodologies, and validation of FDS performance, are considered. The article also delves into safety aspects and presents technical challenges and concerns in FDS for researchers in the field to identify areas requiring further improvement. Finally, future research opportunities to improve fall detection for widespread use are outlined.