In this thesis, we developed an enzyme-free system for colorimetric $Cu^{2+}$ detection, which relies on target-dependent DNAzyme activity and toehold-mediated DNA strand displacement circuit. The system utilizes a DNAzyme, which undergoes self-cleavage in the presence of $Cu^{2+}$. The cleavage of the DNAzyme leads to the production of a catalyst strand that initiates successive toehold-mediated strand displacement reactions. These reactions lead to the release of split G-quadruplex DNAzymes, which are initially caged and inactivated by blocker strands. Fuel strands are incorporated to regenerate the catalyst strands, allowing them to be recycled for multiple cycles of the toehold-mediated strand displacement circuit. Consequently, a large number of active split G-quadruplex DNAzymes are produced and distinct colorimetric signal can be observed. By employing this design principle, $Cu^{2+}$ was sensitively identified with a detection limit of 1.3 nM. Finally, the practical sensing capability of this system was successfully demonstrated by its use to determine $Cu^{2+}$ in tap water.