G-quadruplexes (GQs) are highly stable noncanonical nucleic acid structures that form in the DNA of human cells and play fundamental roles in maintaining genomic stability and regulating gene expression. These unique structures exert broad influence over biologically important processes and can modulate cell survival and human health. In fact, mutations, hyper-stability, and dissociation of GQs are implicated in neurodegenerative disease, mental retardation, premature-aging conditions, and various cancers. As such, GQs are novel drug targets. GQ-targeting therapeutics are developed to influence the folding and genetic interactions of GQs that are implicated in diseased states. To do so requires a greater understanding of GQ structure and dynamics and molecular dynamics (MD) simulations are well suited to provide these fundamental insights. Previous MD simulations of GQs have provided limited information due to inaccuracies in their models, namely the nonpolarizable nature of their force fields (FFs). The cutting-edge Drude polarizable FF models electronic degrees of freedom, allowing charge distribution to change in response to its environment. This is an important component for modeling ion-ion and ion-DNA interactions and can influence the overall stability of GQ structures. The work herein employs the Drude polarizable FF to 1) describe the role of electronic structure on the dynamics and folded stability of GQs, 2) determine the impact of ion interaction on GQ stability, and 3) characterize the role of G-hairpin motifs in GQ intermediates. Such fundamental investigations will help clarify GQs role in healthy and diseased states and transform our understanding of noncanonical DNA, improving human health, therapeutic design, and fundamental science. / Doctor of Philosophy / Human health and disease are influenced by unique nucleic acid structures called G-quadruplexes (GQs). GQs form when DNA or RNA fold into a square-shaped structure that is stabilized by ion interactions and special hydrogen bonding patterns. These GQ structures exert broad influence over normal biological processes, but also play a role in neurodegeneration, intellectual disabilities, premature-aging conditions, and various cancers, many of which are chemotherapeutic resistant. As such, modulating GQ structures, or their interactions with proteins, is a promising therapeutic approach. However, a greater understanding of GQ folding, folded structure, and interactions with other biomolecules is needed to do so. Computational techniques such as molecular dynamics (MD) simulations use experimental data and fundamental biophysics to gain new insights on these properties and inform novel drug design. In this project, we explored the dynamics of several distinct GQ structures and folding intermediates with state-of-the-art MD simulation methods. In doing so, we provided new insight on their structural features as well as their interactions with extended DNA sequences and different ion types, which serve as fundamental information for future structural or computer-aided drug design studies.