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The most relevant aspects of thermodynamics, preparation, crystal structure and superconducting properties under ambient and high pressure of HgBa2Can−1CunO2n+2+δ superconductors are reviewed in this contribution. The ideas which inspired authors to search for the new superconductors among Hg-based complex cuprates are discussed as an example illustrating the benefit of the concept of intergrowth structure formation for the design of new layered materials. Recent results on solid–gas equilibriums useful for reproducible syntheses of different homologues are summarized. The crystal structures are discussed with main attention focused on features such as concentration and location of extra oxygen atoms, static atomic displacements due to partial occupation of oxygen site in a Hg-layer, substitution in a Hg position and a presence of stacking faults. It is shown that these factors have to be taken into account for a correct structure description. The relationships between Tc, doping level, amount and formal charge of extra anions and external pressure are outlined to predict possible paths for enhancement of the superconducting properties in complex cuprates.

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