Access to point-of-care (POC) diagnostics services is essential for ensuring rapid disease diagnosis, management, control, and surveillance. POC testing services can improve access to healthcare especially where healthcare infrastructure is weak and access to quality and timely medical care is a challenge. Improving the accessibility and efficiency of POC diagnostics services, particularly in resource-limited settings, may be a promising route to improving healthcare outcomes. In this review, the accessibility of POC testing is defined as the distance/proximity to the nearest healthcare facility for POC diagnostics service. This review provides an overview of the impact of POC diagnostics on healthcare outcomes in low- and middle-income countries (LMICs) and factors contributing to the accessibility of POC testing services in LMICs, focusing on characteristics of the supply chain management and quality systems management, characteristics of the geographical location, health infrastructure, and an enabling policy framework for POC diagnostics services. Barriers and challenges related to the accessibility of POC diagnostics in LMICs were also discussed. Bearing in mind the reported barriers and challenges as well as the disease epidemiology in LMICs, we propose a lean and agile supply chain management framework for improving the accessibility and efficiency of POC diagnostics services in these settings.