  Spin fluctuations represent the lowest established energy scale in cuprates
and are crucial for the understanding of anomalous normal state properties and
superconductivity in these materials. The memory-function approach to the spin
response in the t-J model is described. Combined with numerical results for
small systems it is able to explain the anomalous scaling at low doping and the
crossover to the Fermi-liquid-like behavior in overdoped systems. Within the
superconducting phase the theory reproduces the resonant peak and its peculiar
double dispersion. Such spin fluctuations are then used as the input for the
theory of superconductivity within the t-J model, where we show that an
important role is played also by the next-nearest-neighbour hopping parameter
$t'$.
