Nucleic acids have been among the first targets for antitumor drugs and antibiotics. With the unveiling of new biological roles in regulation of gene expression, specific DNA and RNA structures have become very attractive targets, especially when the corresponding proteins are undruggable. Biophysical assays to assess target structure as well as ligand binding stoichiometry, affinity, specificity, and binding modes are part of the drug development process. Mass spectrometry offers unique advantages as a biophysical method owing to its ability to distinguish each stoichiometry present in a mixture. In addition, advanced mass spectrometry approaches (reactive probing, fragmentation techniques, ion mobility spectrometry, ion spectroscopy) provide more detailed information on the complexes. Here, we review the fundamentals of mass spectrometry and all its particularities when studying noncovalent nucleic acid structures, and then review what has been learned thanks to mass spectrometry on nucleic acid structures, self-assemblies (e.g., duplexes or G-quadruplexes), and their complexes with ligands.