Disability is defined as a condition of the human body that limits the execution of a task or activity. According to the World Health Organization (WHO), 15% of the world's population suffers from it, recent studies indicate that the growing prevalence are a significant problem and that, consequently, the demand for rehabilitation services is rising considerably. For this reason, different authors propose the use of exoskeletons in rehabilitation therapies as an alternative solution. Thanks to the progress of this kind of technology, it is possible to create robotic systems that help people with disabilities to recover, totally or partially, the original movement of their affected limbs. This Innovative Review Article presents an exhaustive review of the main features of upper-limb exoskeletons such as Degrees of Freedom (DoF), mechanism type, rehabilitation mode, movements allowed, applications and Technology Readiness Level (TRL). Firstly, the study provides a brief description of the biomechanics of the upper limbs of the human body. Next, the material, the rehabilitation modes and the Technology Readiness Level (TRL) of each of these devices are analyzed. As a result, it was observed that aluminum and PLA are the most used materials for exoskeletons' manufacturing. In addition, it was noticed that most of these exoskeletons perform passive rehabilitation. Besides, it was identified that the most common applications are the assistance and rehabilitation in the affected limb of patients who have suffered a stroke. Finally, using TLR scale, it was determined that these mechatronic systems are between TRL5 and TRL8.