G-Quadruplex (G4) DNA (G4 DNA) and RNA (G4 RNA) are secondary nucleic acid structures that have multiple roles in vital cellular processes. G4 DNA- and RNA-binding proteins and unwinding helicases associate with and regulate G4s during virtually all processes that involve DNA and RNA. DEAH-Box helicase 36 (DHX36), a member of the large DExD/H box helicase family, enzymatically unwinds both G4 DNA and G4 RNA. By exerting its G4 helicase function, DHX36 regulates transcription, genomic stability, telomere maintenance, translation and RNA metabolism. This review will provide an overview of G4s and DHX36, including DHX36’s potential role in neuronal development and neurodegeneration. We conclude with a discussion of the possible functions of G4s and DHX36 in the aging brain.