The trend map of the United States shows the large decreases in nitrogen dioxide concentrations tied to environmental regulations from 2005 to 2014. Credits: NASA
Nitrogen dioxide (NO2) (among other pollutants) is emitted by cars, and in the city in the sunlight it splits into nitric oxide (NO) plus an oxygen atom (O) which then combines with an oxygen molecule (O2) to form ozone (O3), a component of smog. (It is more complicated than this - for details see the description of what happens in the troposphere here.) The resulting pollution causes damage to the lungs. Nitrogen dioxide is also given off by power plants and industrial activity.
Volkswagen may have cheated, making its vehicles appear to meet emissions standards when they did not, but others have clearly followed the law. Recent data from NASA shows a drop in NO2 emissions in countries that have introduced regulations, like the USA. Syria's emissions have also reduced, possibly because of the civil war. Countries that have increased their economic activity, like China, have seen increases. The USA and Europe cannot be complacent though - they are still among the biggest polluters, along with China and South Korea and other hotspots around the world. In fact, the UK was recently ordered to reduce NO2 emissions, as they were exceeding European limits, as were 16 other countries.
For more detail, go to NASA's article, New NASA Satellite Maps Show Human Fingerprint on Global Air Quality