Aptamers are synthetic single-stranded DNA or RNA sequences selected from combinatorial oligonucleotide libraries through the well-known in vitro selection and iteration process, SELEX. The last three decades have witnessed a sudden boom in aptamer research, owing to their unique characteristics, like high specificity and binding affinity, low immunogenicity and toxicity, and ease in synthesis with negligible batch-to-batch variation. Aptamers can specifically bind to the targets ranging from small molecules to complex structures, making them suitable for a myriad of diagnostic and therapeutic applications. In analytical scenarios, aptamers are used as molecular probes instead of antibodies. They have the potential in the detection of biomarkers, microorganisms, viral agents, environmental pollutants, or pathogens. For therapeutic purposes, aptamers can be further engineered with chemical stabilization and modification techniques, thus expanding their serum half-life and shelf life. A vast number of antagonistic aptamers or aptamer-based conjugates have been discovered so far through the in vitro selection procedure. However, the aptamers face several challenges for its successful clinical translation, and only particular aptamers have reached the marketplace so far. Aptamer research is still in a growing stage, and a deeper understanding of nucleic acid chemistry, target interaction, tissue distribution, and pharmacokinetics is required. In this review, we discussed aptamers in the current diagnostics and theranostics applications, while addressing the challenges associated with them. The report also sheds light on the implementation of aptamer conjugates for diagnostic purposes and, finally, the therapeutic aptamers under clinical investigation, challenges therein, and their future directions.