Neurology is considered as one of the most challenging fields of medical science due to the complexity of the nervous system in human body. The treatment processes of the patients suffering from neurological disorders are greatly influenced by the advancements in technology. In this regard, the infusion of augmented reality (AR) has immensely improved patients' and healthcare workers' experiences in the field of neurology. Several efforts are being made by the community to introduce various applications of AR for patients as well as for healthcare workers in neurology. This study systematically examines the applications of AR in neurology and synthesizes their uses and impacts in the treatment and assistance of the patients suffering from neurological disorders as well as in the assistance of healthcare workers. The results reveal that most of the AR applications are used for motor disorders while lesser systems are designed for patients with degenerative diseases, most of them being task assistance systems. Moreover, the use of AR applications leaves both long-term and short-term impacts in improving the quality of patient's life. Furthermore, there is a need of introducing more interactive AR systems for patients with degenerative diseases as well as exploring the possibility of using such systems for mental rehabilitation. It has also been identified that there is a potential to develop AR applications for healthcare workers, to train and assist them through simulations. In addition to reviewing the AR applications, this work proposes a taxonomy of AR applications in neurology with different dimensions including scope of AR, type of neurological disorder, and impact of AR assistance on patient's life. Furthermore, this article also highlights challenges the patients with neurological disorders face while using AR applications. Based on the identified challenges, a model has been proposed for application designers and developers to help them develop more useful AR systems. An AR applications architecture has also been suggested for designing the AR systems for patients suffering specifically from degenerative or movement neuro-disorders. Lastly, this article presents some directions for future work in terms of AR usage in neuroscience.