Aptamers are single-stranded DNA or RNA molecules which are submitted to a process denominated SELEX. SELEX uses reiterative screening of a random oligonucleotide library to identify high-affinity binders to a chosen target, which may be a peptide, protein, or entire cells or viral particles. Aptamers can rival antibodies in target recognition, and benefit from their non-proteic nature, ease of modification, increased stability, and pharmacokinetic properties. This turns them into ideal candidates for diagnostic as well as therapeutic applications. Here, we review the recent accomplishments in the development of aptamers targeting emerging viral diseases, with emphasis on recent findings of aptamers binding to coronaviruses. We focus on aptamer development for diagnosis, including biosensors, in addition to aptamer modifications for stabilization in body fluids and tissue penetration. Such aptamers are aimed at in vivo diagnosis and treatment, such as quantification of viral load and blocking host cell invasion, virus assembly, or replication, respectively. Although there are currently no in vivo applications of aptamers in combating viral diseases, such strategies are promising for therapy development in the future.