Four-stranded folded structures, such as G-quadruplexes and i-motifs in the genome, have attracted a growing interest nowadays since they have been discovered in the telomere and in several oncogene promoter regions. Their biological relevance is undeniable since their existence in living cells has been observed. In vivo they take part in the regulation of gene expression, in vitro they are used in the analytical biochemistry. They are attractive and promising targets for cancer therapy. Pressure studies can reveal specific aspects of the molecular processes. Pressure tuning experiments allow the determination of the volumetric parameters of the folded structures and of the folding–unfolding processes. Here, we review the thermodynamic parameters with a special focus on the volumetric ones, which were determined using pressure tuning spectroscopic experiments on the G-quadruplex and i-motif nucleic acid forms.