This feature article addresses the implementation of catalytic nucleic acids as functional units for the construction of logic gates and computing circuits, and discusses the future applications of these systems. The assembly of computational modules composed of DNAzymes has led to the operation of a universal set of logic gates, to field programmable logic gates and computing circuits, to the development of multiplexers/demultiplexers, and to full-adder systems. Also, DNAzyme cascades operating as logic gates and computing circuits were demonstrated. DNAzyme logic systems find important practical applications. These include the use of DNAzyme-based systems for sensing and multiplexed analyses, for the development of controlled release and drug delivery systems, for regulating intracellular biosynthetic pathways, and for the programmed synthesis and operation of cascades.