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We discuss herein the so far reported chiral inorganic and organic superconductors with structural chirality. In chiral inorganic compounds, since the constituent atoms are not stable stereogenic centres, chirality can be reached by breaking improper rotation symmetry in a space group. These systems have anisotropic spin-orbit interaction and are therefore of interest from the viewpoint of the degree of freedom of the Cooper pairs and of the high upper critical magnetic field. We make here the distinction from chiral superconductivity that focuses on the topology of the Cooper pairs. Chiral superconductors derived from their non-centrosymmetric crystalline space groups, despite the achiral nature of the precursors, also exist in organic materials. The chirality induced spin selectivity (CISS) effect has been evidenced in an organic superconductor based on the bis(ethylenedithio)-tetrathiafulvalene (BEDT-TTF) donor. Although there have been reports of superconductivity in alkaline salts of polycyclic aromatic compounds, the existence of the phenomenon has been challenged. These issues are also discussed in this review. Furthermore, chirality can be addressed into organic materials by introducing stereogenic centres, which is a straightforward strategy to prepare chiral organic metals and, a priori, to achieve superconductivity. This review provides as well, besides a description of the structural chiral superconductors known to date, a summary of the main physical effects discovered in these materials, such as the electrical magnetochiral anisotropy (eMChA) and chirality induced spin selectivity (CISS) effects, and the main pieces of evidence reported in support for each of them. [ABSTRACT FROM AUTHOR]

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