Aptamers are oligonucleotides or peptides that are selected from a pool of random sequences that exhibit high affinity toward a specific biomolecular species of interest. Therefore, they are ideal for use as recognition elements and ligands for binding to the target. In recent years, aptamers have gained a great deal of attention in the field of biosensing as the next-generation target receptors that could potentially replace the functions of antibodies. Consequently, it is increasingly becoming popular to integrate aptamers into a variety of sensing platforms to enhance specificity and selectivity in analyte detection. Simultaneously, as the fields of lab-on-a-chip (LOC) technology, point-of-care (POC) diagnostics, and personal medicine become topics of great interest, integration of such aptamer-based sensors with LOC devices are showing promising results as evidenced by the recent growth of literature in this area. The focus of this review article is to highlight the recent progress in aptamer-based biosensor development with emphasis on the integration between aptamers and the various forms of LOC devices including microfluidic chips and paper-based microfluidics. As aptamers are extremely versatile in terms of their utilization in different detection principles, a broad range of techniques are covered including electrochemical, optical, colorimetric, and gravimetric sensing as well as surface acoustics waves and transistor-based detection.