In this work we recall the phenomenon of the superconducting fluctuations. First, we describe the related diamagnetism above the transition temperature Tc in the framework of the Ginzburg-Landau theory, with particular attention to the case of metallic nanoparticles and the diamagnetic magnetization curves M vs H above Tc. Then the case of the high-temperature superconductors is addressed. For optimally doped compounds (having the highest Tc) the conventional theory works well. At variance, dramatic modifications are detected for underdoped compounds, highlighted by e.g. an upturn field in M(H) curves at constant temperature T→Tc+. It is shown that all the anomalies in M(H) and in the magnetic susceptibility vs temperature, are related to the occurrence above Tc of superconducting “islands” lacking long-range coherence because of phase fluctuations in the order parameter. Finally, the case of CaxLa1-xBa1.75-xLa1.25+xCu3O6+y where the hole doping can be obtained by two different channels (oxygen and Ca doping), is analyzed.