The emergence of new states of matter in low-dimensional systems is one of the most intriguing current topics in condensed matter physics. For example, the emergence of magnetism between two nonmagnetic oxides or conductivity and superconductivity between two insulators. Detecting these states is challenging because they come in very small quantities and reside in a buried interface. We use scanning SQUID microscopy to map the small magnetic fields that are generated by localized moments or moving charges. We image a range of electronic behaviors, including nanoscale ferromagnetism, stripy flow of current, and puddles of super-currents.