There is a national framework of Low Emission Zones in Germany. They apply to all motor vehicles except motorcycles. A number of cities also have transit bans on heavy goods vehicle through-traffic. 
There are also some cities (Stuttgart, Darmstadt) that have a zonal driving ban (also incorrectly called 'Dieselfahrverbot' = diesel driving ban). These cities require a minimum standard of Euro 6 diesel to be able to circulate in the streets affected by the zonal driving ban. Other cities may follow.

The national framework for low emission zones means that the only the things that vary from city to city are the location, the emission standard (or sticker) and the times. For the transit bans, the exact definition of the vehicle varies, but all transit bans are for heavy duty vehicles only.

The required sticker can be ordered online from every country either here or there.