We analyze the physical origin and the chemical and biological consequences of the asymmetry that occurs in DNA·RNA hybrids when the purine/pyrimidine (Pu/Py) ratio is different in the DNA and RNA strands. When the DNA strand of the hybrid is Py rich, the duplex is much more stable, rigid, and A-like than when the DNA strand is Pu rich. The origins of this dramatic asymmetry are double: first, the apparently innocuous substitution dT → rU produces a significant decrease in stacking, and second, backbone distortions are larger for DNA(Pu)·RNA(Py) hybrids than for the mirror RNA(Pu)·DNA(Py) ones. The functional impact of the structural and dynamic asymmetry in the biological activities of hybrids is dramatic and can be used to improve the efficiency of antisense-type strategies on the basis of the degradation of hybrids by RNase H or gene editing using CRISPR-Cas9 technology.