The bioinformatics discipline seeks to solve problems in biology with computational theories and methods. Formal concept analysis (FCA) is one such theoretical model, based on partial orders. FCA allows the user to examine the structural properties of data based on which subsets of the data set depend on each other. This paper surveys the current literature related to the use of FCA for bioinformatics. The survey begins with a discussion of FCA, its hierarchical advantages, several advanced models of FCA, and lattice management strategies. It then examines how FCA has been used in bioinformatics applications, followed by future prospects of FCA in those areas. The applications addressed include gene data analysis (with next-generation sequencing), biomarkers discovery, protein-protein interaction, disease analysis (including COVID-19, cancer, and others), drug design and development, healthcare informatics, biomedical ontologies, and phylogeny. Some of the most promising prospects of FCA are: identifying influential nodes in a network representing protein-protein interactions, determining critical concepts to discover biomarkers, integrating machine learning and deep learning for cancer classification, and pattern matching for next-generation sequencing.