Since the first description of the canonical B-form DNA double helix, it has been suggested that alternative DNA, DNA-RNA, and RNA structures exist and act as functional genomic elements. Indeed, over the past few years it has become clear that, in addition to serving as a repository for genetic information, genomic DNA elicits biological responses by adopting conformations that differ from the canonical right-handed double helix, and by interacting with RNA molecules to form complex secondary structures. This review focuses on recent advances on three-stranded (triplex) nucleic acids, with an emphasis on DNA-RNA and RNA-RNA interactions. Emerging work reveals that triplex interactions between noncoding RNAs and duplex DNA serve as platforms for delivering site-specific epigenetic marks critical for the regulation of gene expression. Additionally, an increasing body of genetic and structural studies demonstrates that triplex RNA-RNA interactions are essential for performing catalytic and regulatory functions in cellular nucleoprotein complexes, including spliceosomes and telomerases, and for enabling protein recoding during programmed ribosomal frameshifting. Thus, evidence is mounting that DNA and RNA triplex interactions are implemented to perform a range of diverse biological activities in the cell, some of which will be discussed in this review.