  This is an expanded version of my talk given at the international conference
"Zeldovich-90". I start with a brief recollection of interactions with
Zeldovich in the context of the study of relic gravitational waves. I then
summarise the principles and early results on the quantum-mechanical generation
of cosmological perturbations. The expected amplitudes of relic gravitational
waves are different in different frequency windows, and therefore the
techniques and prospects of their detection are different. One section of the
paper describes the present state of efforts in direct detection of relic
gravitational waves. Another section is devoted to indirect detection via the
anisotropy and polarisation measurements of the cosmic microwave background
radiation (CMB). It is emphasized throughout the paper that the conclusions on
the existence and expected amount of relic gravitational waves are based on a
solid theoretical foundation and the best available cosmological observations.
I also explain in great detail what went wrong with the so-called `inflationary
gravitational waves', whose amount is predicted by inflationary theorists to be
negligibly small, thus depriving them of any observational significance.
