Information systems based on the Internet of Things (IoT) are driving revolutionary solutions in innumerable domains, as the sensitive domain of healthcare. Indicatively, remote monitoring of patients and real-time diagnosis are anticipated as complex systems, offering various services to the associated humans (e.g. patients and caregivers). While researchers focus on the technology necessary to implement remote healthcare systems, such as Remote Elderly Monitoring System (REMS), human concerns restricting their wider adoption are often neglected. Such concerns are transformed into criticalities, that should be considered during system design. In this work, a human-centric perspective on REMS design is explored. Following this perspective, supported tasks are decodified, human concerns associated to REMS usage are identified and revealed criticalities, that stem from human concerns, are extracted. Furthermore, existing REMS implementations are examined, based on the tasks supported and criticalities addressed, resulting in the identification of ways to further improve such systems.