Vehicle emissions contribute to fine particulate matter (PM2.5) and tropospheric ozone air pollution, affecting human health(1-5), crop yields(5,6) and climate(5,7) worldwide. On-road diesel vehicles produce approximately 20 per cent of global anthropogenic emissions of nitrogen oxides (NOx), which are key PM2.5 and ozone precursors(8,9). Regulated NOx emission limits in leading markets have been progressively tightened, but current diesel vehicles emit far more NOx under real-world operating conditions than during laboratory certification testing(10-20). Here we show that across 11 markets, representing approximately 80 per cent of global diesel vehicle sales, nearly one-third of on-road heavy-duty diesel vehicle emissions and over half of on-road light-duty diesel vehicle emissions are in excess of certification limits. These excess emissions (totalling 4.6 million tons) are associated with about 38,000 PM2.5- and ozone-related premature deaths globally in 2015, including about 10 per cent of all ozone-related premature deaths in the 28 European Union member states. Heavy-duty vehicles are the dominant contributor to excess diesel NOx emissions and associated health impacts in almost all regions. Adopting and enforcing next-generation standards (more stringent than Euro 6/VI) could nearly eliminate real-world diesel-related NOx emissions in these markets, avoiding approximately 174,000 global PM2.5- and ozone-related premature deaths in 2040. Most of these benefits can be achieved by implementing Euro VI standards where they have not yet been adopted for heavy-duty vehicles.