Laser-spectroscopic methods of studying nuclei have led to a great deal of systematic experimental information on nuclear properties. The results include nuclear ground and isomeric state spins, magnetic dipole and electric quadrupole moments, and the behaviour of mean square nuclear charge radii within isotopic strings. These data give important information about the single-particle and collective effects on the nuclear structure. This review is devoted to the new generation of experimental laser spectroscopic methods giving access to very weak beams of isotopes far from stability. Special attention is paid to until now poorly investigated regions. They are the following: the exotic proton and neutron-rich low-Z nuclei around the neutron shell closures N = 8, 20; the very interesting calcium region around proton shell closure Z = 20 and with 20 N 28; the neutron-rich medium Z elements and the very high-Z transeinsteinium nuclei.

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