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The electrical conductivity of a material can feature subtle, non-trivial, and spatially varying signatures with critical insight into the material’s underlying physics. Here we demonstrate a conductivity imaging technique based on the atom-sized nitrogen-vacancy (NV) defect in diamond that offers local, quantitative, and non-invasive conductivity imaging with nanoscale spatial resolution. We monitor the spin relaxation rate of a single NV center in a scanning probe geometry to quantitatively image the magnetic fluctuations produced by thermal electron motion in nanopatterned metallic conductors. We achieve 40-nm scale spatial resolution of the conductivity and realize a 25-fold increase in imaging speed by implementing spin-to-charge conversion readout of a shallow NV center. NV-based conductivity imaging can probe condensed-matter systems in a new regime not accessible to existing technologies, and as a model example, we project readily achievable imaging of nanoscale phase separation in complex oxides. [ABSTRACT FROM AUTHOR]