Although nucleic acids primarily function as carriers of the genetic information in biology, their chemical versatility, replicability and programmability render them much more functions inside and outside of cells. Numerous nucleic acid catalysts (known as ribozymes and deoxyribozyme) and binding agents (known as aptamers) have been engineered through the combination of directed evolution and rational design. However, new technologies and theoretical frameworks are still in need to better engineer and utilize these functional nucleic acids in diagnostics and therapeutics. Aiming at engineering more powerful aptazyme-based genetic regulators, we first devised a scheme for direct selection of physiologically active ribozymes in mammalian cells. Model-driven analysis of the selection process showed that the stringency of the selection was strongly influenced by system variables such as degradation rate of un-reacted ribozymes. This analysis led to models that can be exploited to understand and predict the performance of aptazyme-based biosensors and genetic regulators. Several fundamental limitations of aptazymes-based systems were identified from the analyses of these models. As it became apparent that the signals generated by aptazymes need to be processed and amplified at molecular level to have satisfactory effects on the final readouts, we turned our focus to engineering nucleic acid-based signal processors using several newly invented schemes such as ‘entropy-driven DNA amplifier’ and ‘catalyzed DNA self-assembly.’ We first demonstrated a method to couple entropy-driven DNA amplifiers to allosteric deoxyribozymes, and then proved that the concept of catalyzed DNA self-assembly can be used to design efficient and versatile signal amplifiers for analytical applications on various platforms. These developments may potentially lead to sensitive, low-cost, and point-of-care diagnostic devices. Taken together, these works not only addressed several important issues regarding the engineering and application of nucleic acid catalysts, but also revealed a new theme in molecular engineering: In order to better engineer and utilize a part, one needs to characterize, model, and modify the system surrounding the part so that the potential of the part can be maximized. / text