An aptamer is a synthetic oligonucleotide, referring to a single-stranded deoxyribonucleic acid or ribonucleic acid ligand produced by synthesis from outside the body using systematic evolution of ligands by exponential enrichment (SELEX) technology. Owing to their special screening process and adjustable tertiary structures, aptamers can bind to multiple targets (small molecules, proteins, and even whole cells) with high specificity and affinity. Moreover, due to their simple preparation and stable modification, they have been widely used to construct biosensors for target detection. The paper-based sensor is a product with a low price, short detection time, simple operation, and other superior characteristics, and is widely used as a rapid detection method. This review mainly focuses on the screening methods of aptamers, paper-based devices, and applicable sensing strategies. Furthermore, the design of the aptamer-based lateral flow assay (LFA), which underlies the most promising devices for commercialization, is emphasized. In addition, the development prospects and potential applications of paper-based biosensors using aptamers as recognition molecules are also discussed.