  Superconducting properties of metallic nanowires can be entirely different
from those of bulk superconductors because of the dominating role played by
thermal and quantum fluctuations of the order parameter. For superconducting
wires with diameters below $ \sim 50$ nm quantum phase slippage is an important
process which can yield a non-vanishing wire resistance down to very low
temperatures. Further decrease of the wire diameter, for typical material
parameters down to $\sim 10$ nm, results in proliferation of quantum phase
slips causing a sharp crossover from superconducting to normal behavior even at
T=0. A number of interesting phenomena associated both with quantum phase slips
and with the parity effect occur in superconducting nanorings. We review recent
theoretical and experimental activities in the field and demonstrate dramatic
progress in understanding of the phenomenon of superconductivity in
quasi-one-dimensional nanostructures.
