Bioelectronic devices have been researched widely because of their potential applications, such as information storage devices, biosensors, diagnosis systems, organism-mimicking processing system cell chips, and neural-mimicking systems. Introducing biomolecules including proteins, DNA, and RNA on silicon-based substrates has shown the powerful potential for granting various functional properties to chips, including specific functional electronic properties. Until now, to extend and improve their properties and performance, organic and inorganic materials such as graphene and gold nanoparticles have been combined with biomolecules. In particular, bionanohybrid materials that are composed of biomolecules and other materials have been researched because they can perform core roles of information storage and signal processing in bioelectronic devices using the unique properties derived from biomolecules. This review discusses bioelectronic devices related to computation systems such as biomemory, biologic gates, and bioprocessors based on bionanohybrid materials with a selective overview of recent research. This review contains a new direction for the development of bioelectronic devices to develop biocomputation systems using biomolecules in the future.