Ambient Assisted Living is a concept that focuses on using technology to support and enhance the quality of life and well-being of frail or elderly individuals in both indoor and outdoor environments. It aims at empowering individuals to maintain their independence and autonomy while ensuring their safety and providing assistance when needed. Human Activity Recognition is widely regarded as the most popular methodology within the field of Ambient Assisted Living. Human Activity Recognition involves automatically detecting and classifying the activities performed by individuals using sensor-based systems. Researchers have employed various methodologies, utilizing wearable and/or non-wearable sensors, and employing algorithms ranging from simple threshold-based techniques to more advanced deep learning approaches. In this review, literature from the past decade is critically examined, specifically exploring the technological aspects of Human Activity Recognition in Ambient Assisted Living. An exhaustive analysis of the methodologies adopted, highlighting their strengths and weaknesses is provided. Finally, challenges encountered in the field of Human Activity Recognition for Ambient Assisted Living are thoroughly discussed. These challenges encompass issues related to data collection, model training, real-time performance, generalizability, and user acceptance. Miniaturization, unobtrusiveness, energy harvesting and communication efficiency will be the crucial factors for new wearable solutions.