Transport currents can flow in unexpected ways through a sample,  particularly in dissipationless conductors. In this talk, I will discuss how we use a magnetic probe to understand how electrical conduction happens in two types of dissipationless conductors. First, we study microstructures fabricated from a heavy-fermion superconductor that exhibit unusual resistive superconducting transitions. We show that this behavior is explained by a spatially modulated transition temperature, and we discover that local strain is the cause of the spatial modulation. Second, we visualize how a non-equilibrium current flows in a quantum anomalous Hall insulator by imaging the magnetic field produced by the current. Surprisingly, we find that the current can flow in the bulk of the sample within the quantized regime.