Chronic and non-communicable diseases (NCDs) account for a large proportion of global disorders and mortality, posing significant burdens on healthcare systems. Early diagnosis and timely interference are critical for effective management and disease prevention. However, the traditional methods of diagnosis still suffer from high costs, time delays in processing, and infrastructure requirements that are usually unaffordable in resource-constrained settings. Aptamer-based biosensors have emerged as promising alternatives to offer enhanced specificity, stability, and cost-effectiveness for disease biomarker detection. The SELEX (Systematic Evolution of Ligands by Exponential Enrichment) methodology allows developing aptamers with high-affinity binding capabilities to a variety of targets, for instance proteins, cells, or even small molecules, hence rendering them suitable for NCD diagnosis. Aptasensors—recent developments in the electrochemical and optical dominion—offer much enhanced sensitivity, selectivity, and stability of detection across a diverse range of diseases from lung cancer and leukemia to diabetes and chronic respiratory disorders. This study provides a comprehensive review of progress in aptamer-based sensors, focusing on their role in point-of-care diagnostics and adaptability in a real-world environment with future directions in overcoming current limitations.