Passenger cars are an important source of air pollution, especially in urban areas. Recently, real-driving emissions (RDE) test procedures have been introduced in the EU aiming to evaluate nitrogen oxides (NOx) and particulate number (PN) emissions from passenger cars during on-road operation. Although RDE accounts for a large variety of real-world driving, it excludes certain driving situations by setting boundary conditions (e.g., in relation to altitude, temperature or dynamic driving). The present work investigates the on-road emissions of NOx, NO2, CO, particle number (PN) and CO2 from a fleet of 19 Euro 6b, 6c and 6d-TEMP vehicles, including diesel, gasoline (GDI and PFI) and compressed natural gas (CNG) vehicles. The vehicles were tested under different on-road driving conditions outside boundaries. These included 'baseline' tests, but also testing conditions beyond the RDE boundary conditions to investigate the performance of the emissions control devices in demanding situations. Consistently low average emission rates of PN and CO were measured from all diesel vehicles tested under most conditions. Moreover, the tested Euro 6d-TEMP and Euro 6c diesel vehicles met the NOx emission limits applicable to Euro 6d-TEMP diesel vehicles during RDE tests (168 mg/km). The Euro 6b GDI vehicle equipped with a gasoline particulate filter (GPF) presented PN emissions < 6 × 1011 #/km. These results, in contrast with previous on-road measurements from earlier Euro 6 vehicles, indicate more efficient emission control technologies are currently being used in diesel and gasoline vehicles. At the same time, the results suggest that particular attention should be given to CO and PN emissions of certain types of vehicles when driven under dynamic conditions, and possibly additional work is necessary. In particular, the emissions of CO (measured in this study during the regulated RDE test, but without an emission limit associated to it) or PN from PFI vehicles (presently not covered by the Euro 6 standard) showed elevated results in some occasions. Emissions of CO were up to 7.5 times higher when the more dynamic tests were conducted and the highest PN emissions were measured from a PFI gasoline vehicle during dynamic driving. Although based on a limited sample of cars, our work points to the relevance of a technology- and fuel-neutral approach to vehicle emission standards, whereby all vehicles must comply with the same emission limits for all pollutants.