Competition between electronic orders with similar energy scales can give rise to complex emergent behaviors. Detecting traces of such orders requires versatile probes that access different aspects of the system, such as conductivity, superconductivity, and magnetism. I will describe several material systems where a local view uncovered surprising mesoscopic effects. I will also discuss recent advances in phase-sensitive measurements and phase mapping, including studies of tunable Josephson junction arrays as a model platform for emergent phenomena. Examples include two polymorphs of tantalum disulfide, a van der Waals material: 4Hb-TaS2, in which we identified a hidden magnetic phase, and the 1T polymorph, where we probed a hidden metallic state embedded in an insulator. These results demonstrate the power of a local phase-sensitive view in probing quantum materials.