The smart grid was initially developed to facilitate communication between operators of the electric power system (such as power generation companies and transmission system operators) and consumers within the distribution network. To implement the smart grid paradigm, time-synchronized measurement devices were developed and introduced into the electric power system. Phasor measurement units (PMUs) and waveform measurement units (WMUs) were created for wide-area transmission networks (at the high-voltage layer), while micro-PMUs were introduced for real-time state estimation in distribution networks (at the low-voltage layer). These time-synchronized measurement devices allow power system operators to monitor the operational status of power generation, transmission, and distribution infrastructure in real time. In particular, data-driven applications utilizing the measurement data can intelligentize and advance the monitoring, operation, and control of the smart grid. The capabilities of digitized high-resolution measurement and time-synchronization are the key factors that enable these contributions to the smart grid. This paper provides an introduction to time-synchronized measurement devices, outlines their specific capabilities, and explores the data-driven applications that can be implemented for advanced smart grid monitoring systems.