Instrument transformers (ITs) play a key role in electrical power systems, facilitating the accurate monitoring and measurement of electrical quantities. They are essential for measurement, protection, and metering in transmission and distribution grids and accurately reducing the grid voltage and current for low-voltage input instrumentation. With the increase in renewable energy sources, electronic converters, and electric vehicles connected to power grids, ITs now face challenging distorted conditions that differ from the nominal ones. The study presented in this paper is a collaborative work between national metrology institutes and universities that analyzes IT performance in measuring distorted voltages and currents in medium-voltage grids under realistic conditions. Both current and voltage measuring transformers are examined, considering influence quantities like the temperature, mechanical vibration, burden, adjacent phases, and proximity effects. The study provides detailed insights into measurement setups and procedures, and it quantifies potential errors arising from IT behavior in measuring distorted signals in the presence of the various considered influence quantities and their combinations. The main findings reveal that the temperature has the most evident impact on the inductive voltage transformer performance, as well as the burden, causing significant changes in ratio error and phase displacement at the lower temperatures. As for low-power ITs, establishing a priori the effects of adjacent phases and proximity on the frequency responses of low-power ITs is a complex matter, because of their different characteristics and construction solutions.