CONSPECTUS: The successes of electronic digital logic have transformed every aspect of human life over the last half-century. The word "computer" now signifies a ubiquitous electronic device, rather than a human occupation. Yet evidently humans, large assemblies of molecules, can compute, and it has been a thrilling challenge to develop smaller, simpler, synthetic assemblies of molecules that can do useful computation. When we say that molecules compute, what we usually mean is that such molecules respond to certain inputs, for example, the presence or absence of other molecules, in a precisely defined but potentially complex fashion. The simplest way for a chemist to think about computing molecules is as sensors that can integrate the presence or absence of multiple analytes into a change in a single reporting property. Here we review several forms of molecular computing developed in our laboratories. When we began our work, combinatorial approaches to using DNA for computing were used to search for solutions to constraint satisfaction problems. We chose to work instead on logic circuits, building bottom-up from units based on catalytic nucleic acids, focusing on DNA secondary structures in the design of individual circuit elements, and reserving the combinatorial opportunities of DNA for the representation of multiple signals propagating in a large circuit. Such circuit design directly corresponds to the intuition about sensors transforming the detection of analytes into reporting properties. While this approach was unusual at the time, it has been adopted since by other groups working on biomolecular computing with different nucleic acid chemistries. We created logic gates by modularly combining deoxyribozymes (DNA-based enzymes cleaving or combining other oligonucleotides), in the role of reporting elements, with stem-loops as input detection elements. For instance, a deoxyribozyme that normally exhibits an oligonucleotide substrate recognition region is modified such that a stem-loop closes onto the substrate recognition region, making it unavailable for the substrate and thus rendering the deoxyribozyme inactive. But a conformational change can then be induced by an input oligonucleotide, complementary to the loop, to open the stem, allow the substrate to bind, and allow its cleavage to proceed, which is eventually reported via fluorescence. In this Account, several designs of this form are reviewed, along with their application in the construction of large circuits that exhibited complex logical and temporal relationships between the inputs and the outputs. Intelligent (in the sense of being capable of nontrivial information processing) theranostic (therapy + diagnostic) applications have always been the ultimate motivation for developing computing (i.e., decision-making) circuits, and we review our experiments with logic-gate elements bound to cell surfaces that evaluate the proximal presence of multiple markers on lymphocytes.