In the research of advanced materials based on nanoscience and nanotechnology, it is often desirable to measure nanoscale local electrical conductivity at a designated position of a given sample. For this purpose, multiple-probe scanning probe microscopes (MP-SPMs), in which two, three or four scanning tunneling microscope (STM) or atomic force microscope (AFM) probes are operated independently, have been developed. Each probe in an MP-SPM is used not only for observing high-resolution STM or AFM images but also for forming an electrical contact enabling nanoscale local electrical conductivity measurement. The world's first double-probe STM (DP-STM) developed by the authors, which was subsequently modified to a triple-probe STM (TP-STM), has been used to measure the conductivities of one-dimensional metal nanowires and carbon nanotubes and also two-dimensional molecular films. A quadruple-probe STM (QP-STM) has also been developed and used to measure the conductivity of two-dimensional molecular films without the ambiguity of contact resistance between the probe and sample. Moreover, a quadruple-probe AFM (QP-AFM) with four conductive tuning-fork-type self-detection force sensing probes has been developed to measure the conductivity of a nanostructure on an insulating substrate. A general-purpose computer software to control four probes at the same time has also been developed and used in the operation of the QP-AFM. These developments and applications of MP-SPMs are reviewed in this paper.