NMR and NQR spectra and spin-lattice relaxation measurements carried out in LASCO and YBCO-type crystals are presented and analyzed in order to derive insights on the correlations and spin-dynamics of the Cu2+ ions and on the microscopic mechanisms of high-T c superconductivity. As an illustrative example on how the magnetic correlation length and spin dynamics properties can be extracted from the relaxation rateW, the35Cl NMR data in the two-dimensional Heisenberg system Sr2CuCl2O2, around the paramagnetic-antiferromagnetic (PA-AF) transition are first considered. Then the139La NQR relaxation measurements in La2−xSrxCuO4 are briefly reviewed and it is shown how a simple picture of localized Cu2+ magnetic moments, whose spin fluctuation times are controlled by the charge defects induced by the doping, leads in a direct way to quantitative estimates for the progressive shift, on cooling, of the spectral density of the low-frequency spin excitations towards the high frequency range. This phenomenon can be described in terms of effective spin at the Cu2+ ions, and its similarities with the analogous effect of progressive delocalization in Heavy Fermions systems are pointed out. Thus, the superconducting transition appears to occur in an unconventional Fermi liquid with AF correlations among itinerant pseudoparticles, possibly involving a mechanism not directly related to the magnetic correlated dynamics. In fact, a universal behavior of the relaxation rates as a function of temperature is observed, regardless of the transition temperatureT c. The independence ofT c from the low frequency static and dynamical spin properties is also indicated by89Y Knight shifts and from63Cu relaxation rates in systems like YBa2Cu4O8 (Y124), whereT c can be changed by atomic substitutions and by controlling the oxygen stoichiometry. The effect of an external magnetic field on the correlated spin dynamics of the AF Fermi liquid is investigated and from a comparison of Cu NQR relaxation and NMR relaxation in oriented powder of YBCO and LASCO it is shown that the external field has the small but unambiguous effect of depressing the relaxation rates aboveT c, besides strongly enhancing them in the superconducting phase. A maximum in the ratio $${{W\left( {NQR} \right)} \mathord{\left/ {\vphantom {{W\left( {NQR} \right)} {W\left( {\vec H\left\| {\vec c} \right.} \right)}}} \right. \kern-\nulldelimiterspace} {W\left( {\vec H\left\| {\vec c} \right.} \right)}}$$ is thus observed around 80 K, either in LASCO or in YBCO, again indicating that the transition could be driven by a mechanism not directly involving the spin dynamic properties. To study the role of the fluxions belowT c 89Y NMR shifts and spectra in oriented powders of YBCO are analyzed. Information on the spin susceptibility and on the structure of the vortex lattice is obtained. In addition, from the temperature behavior of the linewidth a motional narrowing related to flux melting is evidenced. The effective correlation time for the vortex motion is derived and it is discussed why μ+SR cannot detect it in view of the different rigid-lattice line broadening.