Superconducting (SC) fluctuations were discovered at the end of the 1960s and have since become an important research area in superconductivity. Fluctuations of the SC state are manifested in a variety of phenomena and are therefore of great fundamental and practical importance. By understanding their physics, it was possible to elucidate underlying properties of the SC state itself.
With the discovery of cuprate oxide superconductors (high-temperature superconductors, HTS) the interest in SC fluctuation phenomena was further enhanced. In these materials, superconducting fluctuations manifest themselves in a wide range of temperatures due to the extremely short coherence lengths and low effective dimensionality of the electron system. Moreover, anomalous properties of the normal state of certain HTS were attributed to strong fluctuations in these systems. Being studied in the framework of the phenomenological Ginzburg- Landau theory and, more extensively, in the diagrammatic microscopic approach based on the BCS theory, SC fluctuations as well as other quantum contributions (weak localization, etc.), became a new tool for the investigation and characterization of such new systems as disordered electron systems, granular metals, Josephson structures, artificial super-lattices, some HTS, etc. The characteristic feature of SC fluctuations is their strong dependence on temperature and magnetic field in the vicinity of the phase transition. This allows for the separation of fluctuation effects from other contributions and for their use as a source of information about microscopic parameters of a material, first and foremost the critical temperature and the zero-temperature critical magnetic field. SC fluctuations are very sensitive to relaxation processes breaking the phase coherence and, therefore, can be used for a versatile characterization of SCs. This fluctuation spectroscopy approach has recently been developed into a powerful tool for studying properties of superconducting systems on a quantitative level.
Here we review the physics of SC fluctuations starting from a qualitative description of both, thermodynamic fluctuations close to the critical temperature and quantum fluctuations at zero temperature in the vicinity of the second critical field. The analysis of the latter allows us to present the scenario of fluctuation formation as fragmentation of the Abrikosov lattice. The review consists of the presentation of a series of experimental findings, their microscopic description and the numerical analysis of the effects of fluctuations on a variety of the properties of SCs in the entire phase diagram beyond the superconducting phase.