The integration of advanced measuring technologies in distribution systems allows distribution system operators to have better observability of dynamic and transient events. In this work, the applications of distribution grid measurement technologies are explored in detail. The main contributions of this review are: (a) a comparison of eight advanced measurement devices for distribution networks, based on their technical characteristics, including reporting periods, measuring data, precision, and sample rate; (b) a review of the most recent applications of micro-Phasor Measurement Units, Smart Meters, and Power Quality Monitoring devices used in distribution systems, considering different novel methods applied for data analysis; and (c) an input-output table that relates measured quantities from micro-Phasor Measurement Units and Smart Meters needed for each specific application found in this extensive review. This paper aims to serve as an important guide for researches and engineers studying smart grids.