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While in XX century the theory of superconductivity has focused on ahomogeneous metal with a rigid lattice which can be reduced to a singleeffective conduction band in the dirty limit. Today in the XXI century, thephysics of superconductivity is focusing on complexity of quantum matter wherenovel quantum functionalities with lattice inhomogeneity at nanoscale (between1 nm and 100 nm) and at mesoscopic scale (in the range 100-10000 nm), where theelectronic structure need to be described by multiple Fermi surfaces andmultiple gaps in the superconducting phase in the clean limit. The presentissue of Journal of superconductivity and Novel magnetism collects paperspresented at the International Conference Superstripes 2019 which was held onJune 23-29, 2019, in Ischia Island, Italy. The series of Stripes conferencestarted on Dec 8 1996 and it has contributed to scientific advances in the newphysics of superconductivity in quantum complex systems in these last 23 yearswhere polarons, strain, multigap superconductivity, exchange interactionbetween condensates, granular superconductivity and percolation play a keyrole. The articles collected in this issue cover hot topics of the new quantumphysics of complex matter including the mechanism of high temperaturesuperconductivity, complex magnetic orders and orbital physics in stronglycorrelated materials which have been growing rapidly in these last two yearsopening new perspectives also in mesoscopic quantum engineering.

Superconductivity in Quantum Complex Matter: the Superstripes Landscape