Neurological disorders, including stroke, spinal cord injuries, multiple sclerosis, and Parkinson's disease, generally lead to diminished upper extremity (UE) function, impacting individuals' independence and quality of life. Traditional assessments predominantly focus on standardized clinical tasks, offering limited insights into real-life UE performance. In this context, this review focuses on wearable technologies as a promising solution to monitor UE function in neurologically impaired individuals during daily life activities. Our primary objective is to categorize the different sensors, data collection and data processing approaches employed. What comes to light is that the majority of studies involved stroke survivors, and predominantly employed inertial measurement units and accelerometers to collect kinematics. Most analyses in these studies were performed offline, focusing on activity duration and frequency as key metrics. Although wearable technology shows potential in monitoring UE function in real-life scenarios, an ideal solution that combines non-intrusiveness, lightweight design, detailed hand and finger movement capture, contextual information, extended recording duration, ease of use, and privacy protection remains an elusive goal. Furthermore, it stands out a growing necessity for a multimodal approach in capturing comprehensive data on UE function during real-life activities to enhance the personalization of rehabilitation strategies and ultimately improve outcomes for these individuals.