It has long been known that temporal correlations exist between tunneling electrons in nanoscale electrical devices. Still, electron dynamics in quantum dots and other nanostructures have usually been inferred from dc measurements rather than observed directly. We have recently addressed this problem by fabricating a quantum dot with an integrated radio-frequency single-electron transistor (RF-SET) charge detector, and have used the RF-SET to observe individual electron tunneling events on the quantum dot in real time. Detecting the motion of individual electrons in a quantum dot allows direct access to dynamical information, and allows electron counting experiments analogous to the photon counting experiments of quantum optics. It also demonstrates that the RF-SET can be used for single-shot measurement of the charge state of an isolated nanostructure, with important implications for solid-state quantum computation. By extending these techniques to more complex nanostructures, we can also investigate such issues as the quantum measurement problem, detection of individual electronic spins, and development of a current standard based on electron counting.