Since the discovery of DNA, researchers have been attempting to decode the detailed structure, properties, and abilities of this molecule. At first approximation, DNA can be thought of as a long, regular, double-stranded helix encoding the genomic information of life. However, on closer analysis DNA has been found to take on a wide variety of complex shapes and functions both in vitro and in vivo. DNA can be single-, double-, triple-, and even quadruple-stranded in nature and can bind in both the Watson-Crick conformations and also in a variety of non-canonical con- figurations that add to its inherent flexibility, structure, and activity. Elucidating the varied structures and behaviors of DNA has historically been an experimental endeavor, due in large part to the difficulties in capturing nucleic acid's complex mo- tions and function in a tractable computational model. However, as the applications of DNA expand and computation power increases, simulation models are playing an increasingly important role in DNA understanding and engineering. In this thesis, we simulate short DNA and RNA (less than 100 nucleotides) and examine their complex structures. In particular, we will (i) experimentally evaluate previous DNA coarse grained models for their ability to capture complex nucleic acid structures, and (ii) develop a new model that can better capture both canonical and non-canonical in- teractions and show its utility in the study of several known structures. Further, we will use our understanding of the intricate interactions of short oligonucleotides to unravel a hereto experimentally inaccessible mechanistic pathway for a catalytically active DNA molecule. The model developed and the importance of non-canonical interactions in nucleic acid systems will be useful in the continued understanding and engineering of DNA and RNA molecules for nanotechnology, genetic engineering, and therapeutic applications.