Neurological disorders are the leading cause of global disability. However, for most people around the world, current neurological care is poor. In low-income countries, most individuals lack access to proper neurological care, and in high-income countries, distance and disability limit access. With the global proliferation of smartphones, teleneurology - the use of technology to provide neurological care and education remotely - has the potential to improve and increase access to care for billions of people. Telestroke has already fulfilled this promise, but teleneurology applications for chronic conditions are still in their infancy. Similarly, few studies have explored the capabilities of mobile technologies such as smartphones and wearable sensors, which can guide care by providing objective, frequent, real-world assessments of patients. In low-income settings, teleneurology can increase the capacity of local care systems through professional development, diagnostic support and consultative services. In high-income settings, teleneurology is likely to promote the expansion and migration of neurological care away from institutions, incorporate systems of asynchronous communication (such as e-mail), integrate clinicians with diverse skill sets and reach new populations. Inertia, outdated policies and social barriers - especially the digital divide - will slow this progress at considerable cost. However, a future increasingly will be possible in which neurological care can be accessed by anyone, anywhere. Here, we examine the emerging evidence regarding the benefits of teleneurology for chronic conditions, its role and risks in low-income countries and the promise of mobile technologies to measure disease status and deliver care. We conclude by discussing the future trends, barriers and timing for the adoption of teleneurology.