G-Quadruplex (G4) is one of the higher-order structures occurring in guanine-rich sequences of nucleic acids, and plays critical roles in biological processes. The G4-forming sequences can generate three kinds of topologies, i.e., parallel, anti-parallel, and hybrid, and these polymorphic structures have an important influence on G4-related biological functions. In this review, we highlight variety of structures generated by G4s containing various sequences and under diverse conditions. We also discuss the G4 ligands which induce specific topologies and/or conversion between different topologies. (C) 2020 Elsevier Inc. All rights reserved.