Electronic systems present a variety of behaviors due to interactions and correlations of electrons with other electrons or with the host material. These electronic states are few of the most fascinating topics in condensed matter physics. For instance, interfaces between certain non-magnetic insulators give rise to tunable metallic, superconducting, and magnetic states, which are still far from being understood. Other examples are topological insulators that feature dissipationless conductivity at the edges, or the behavior near quantum critical points.

 By tracking the spatial distribution of electronic states, local imaging techniques contribute a lot to the understanding of correlated electrons behavior. We use a local magnetic imaging technique, scanning SQUID microscopy, to track the spatial distribution of electronic states near surfaces and interfaces. I will describe our recent efforts to map the electronic behavior at Strontium titanate-based interfaces and their response to external stimuli. Additionally, I will present a local view of the current flow near a metal to insulator transition and local dynamics of a superconductor to insulator transition near a quantum critical point.