The novel phenomenon of chiral tunneling in metallic single-wall carbon nanotubes is considered. It is induced by the interplay of electrostatic and pseudomagnetic effects in electron scattering in chiral nanotubes and is characterized by an oscillatory dependence of the electron transmission probability on the nanotube chiral angle and the strength of the scattering potential. The appearance of a special (Aharonov-Bohm-like) phase in chiral tunneling affects various phase-coherent phenomena in nanostructures. We examine chiral effects in: (i) persistent currents in circular nanotubes, (ii) Josephson currents in nanotube-based SNS junctions, and (iii) resonant electron tunneling through chiral nanotube-based quantum dots. © 2010 American Institute of Physics.