Nucleic acids are natural macromolecules with the ability to store and transmit information based on the strict base-pairing principle. Beyond the natural nucleic acid double helixes, various DNA/RNA nanostructures with customized geometries and functionalities have been fabricated. Featured with programmability and sequence-dependent responsiveness, DNA/RNA nanostructures have been employed for the rational design and construction of logic devices. When stimulated by internal molecular triggers and/or external stimuli, these logic gate devices can operate at nanoscale level in complex biological environments, performing logic operations and producing corresponding outputs. In this minireview, we summarize the recent advances of nucleic acid logic devices, which are responsive to various stimuli, including DNA/RNA strands, metal ions, small molecules, peptides, proteins, photo-irradiation, pH changes, and so forth. The applications of these devices in biosensing and biofunction regulation are also included. In the last part of the present study, we discuss the remaining challenges and perspectives of nucleic acid logic devices.