Aptamers are target specific ssDNA, RNA or peptide sequences generated by an in vitro selection and amplification method called SELEX (Systematic Evolution of Ligands by EXponential Enrichment), which involves repetitive cycles of binding, recovery and amplification steps. Aptamers have the ability to bind with a variety of targets such as drugs, proteins, heavy metals, and pathogens with high specificity and selectivity. Aptamers are similar to monoclonal antibodies regarding their binding affinities, but they offer a number of advantages over the existing antibody-based detection methods, which make the aptamers promising diagnostic and therapeutic tools for future biomedical and analytical applications. The aim of this review article is to provide an overview of the recent advancements in aptamer screening methods along with a concise description of the major application areas of aptamers including biomarker discovery, diagnostics, imaging and nanotechnology.