Colloquium: Linear in temperature resistivity and associated mysteries including high temperature superconductivity

Even after much research and heated debate, high temperature superconductivity remains one of the most challenging and controversial problems in condensed matter. Apart from that at a phenomenological level some accepted and successful paradigms for the behavior of electrons fail, even the model relevant for the observed properties has been under debate, as well as methods to solve any model satisfactorily. In this Colloquium a perspective is provided into issues involved and results of a systematic solution on a model are reviewed and compared with experiments on an anomalous metallic state which is the basis for the emerging superconducting state.