Cognitive computing technologies are gradually becoming integrated with remote healthcare systems in the last years, exhibiting promising capabilities to revolutionize patient care delivery even in remote or underserved areas. In this paper, a wide study of the literature in which cognitive computing is applied to remote healthcare, so covering a few domains like diagnostic support, remote monitoring, personalized treatment planning, virtual assistants, health data analysis, natural language processing, decision support systems, medical imaging analysis, and remote education and training is presented. Based upon a systematic review of the existing research findings, this paper summarizes the current technological superiority, identifying the pros and cons of the cognitive computing utilization in distributed medical institutions. Moreover, the review highlights future research directions in the area such as data privacy concerns addressed, regulatory compliance, algorithm bias, and interdisciplinary collaboration between healthcare professionals and technologists. Through potential of cognitive computing in enhancing the precision and accuracy of diagnosis, improving patient healthcare, and reducing healthcare costs considerably in remote settings, this paper indeed provides useful information for researchers, practitioners, and stakeholders in the advancement of remote healthcare.