With the number of people surviving a stroke soaring, automated upper limb impairment assessment has been extensively investigated in the past decades since it lays the foundation for personalised precision rehabilitation. The recent advancement of sensor systems, such as high-precision and real-time data transmission, have made it possible to quantify the kinematic and physiological parameters of stroke patients. In this paper, we review the development of sensor-based upper limb quantitative impairment assessment, concentrating on the capable of comprehensively and accurately detecting motion parameters and measuring physiological indicators to achieve the objective and rapid quantification of the stroke severity. The paper discusses various features used by different sensors, detectable actions, their utilization techniques, and effects of sensor placement on system accuracy and stability. In addition, both the advantages and disadvantages of the model-based and model-free algorithms are also reviewed. Furthermore, challenges encompassing comprehensive assessment of medical scales, neurological deficits assessment, random movement detection, the effect of the sensor placement, and the effect of the number of sensors are also discussed.