This article provides a general overview of the bio-inspired computing method called DNA-Based Computing (DBC), including its theory and applications. The main theme of DBC is the central dogma of molecular biology (once information of DNA/RNA has got into a protein, it can’t get out again), i.e., DNA to RNA (sequences of four types of nucleotides) and DNA/RNA to protein (sequence of twenty types of amino acids) are allowed, not the reverse ones. Thus, DBC transfers few-element information (DNA/RAN-like) to many-element information (protein-like), solving a given cognitive problem. DBC can take many forms; this article elucidates two main forms, denoted as DBC-1 and DBC-2. Using arbitrary numerical examples, it is shown that DBC-1 can solve the following cognitive problems: “similarity indexing between seemingly different but inherently identical objects” and “recognizing regions of an image separated by a complex boundary.” DBC-2 can solve the following cognitive problem: “pattern recognition when the relevant information is insufficient.” Smart manufacturing-based systems (digital twins and big data analytics) must solve the abovementioned problems to make the manufacturing enablers (machine tools and monitoring systems) more self-reliant and autonomous. Consequently, DBC can improve the cognitive problem-solving ability of smart manufacturing-relevant systems and, thereby, can enhance its biologicalization.