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In this brief overview we discuss the principal features of real spacepairing as expressed via corresponding low-energy (t-J or periodicAnderson-Kondo) effective Hamiltonian, as well as consider concrete propertiesof those unconventional superconductors. We also rise the basic question ofstatistical consistency within the so-called renormalized mean-field theory. Inparticular, we provide the phase diagrams encompassing the stable magnetic andsuperconducting states. We interpret real space pairing as correlated motion offermion pair coupled by short-range exchange interaction of magnitude Jcomparable to the particle renormalized band energy $\sim tx$, where $x$ is thecarrier number per site. We also discuss briefly the difference between thereal-space and the paramagnon - mediated sources of superconductivity. Thepaper concentrates both on recent novel results obtained in our research group,as well as puts the theoretical concepts in a conceptual as well as historicalperspective. No slave-bosons are required to formulate the present approach.

acta physica polonica. a

Theory of Unconventional Superconductivity in Strongly Correlated  Systems: Real Space Pairing and Statistically Consistent Mean-Field Theory -  in Perspective