The EU's role is to oversee the running of the police, the courts and the customs service in Kosovo.
When it is at its full strength in a few months it will have almost 2,000 international staff.
They are taking over many of the duties from the United Nation's mission in Kosovo, Unmik.
It means that after almost a decade in charge, the UN is leaving and will only retain a small political role.
The new EU officials with their big blue and yellow armbands now have a visible presence in Kosovo's capital.
Serb opposition
The deployment started bright and early on Tuesday morning.
In Gracanica, the Serb-dominated town in central Kosovo, police officers from the EU mission met their counterparts.
The visit at the regional police station didn't last long, but it was symbolic.
When it is at its full strength in a few months it will have almost 2,000 international staff.
They are taking over many of the duties from the United Nation's mission in Kosovo, Unmik.
It means that after almost a decade in charge, the UN is leaving and will only retain a small political role.
The new EU officials with their big blue and yellow armbands now have a visible presence in Kosovo's capital.
Serb opposition
The deployment started bright and early on Tuesday morning.
In Gracanica, the Serb-dominated town in central Kosovo, police officers from the EU mission met their counterparts.
The visit at the regional police station didn't last long, but it was symbolic.
Eulex has been opposed by many Kosovo Serbs.
But a handshake between the Serb police commander and an EU official sent out a signal that the Kosovo Serb police officers are willing to work with the new mission.
But a handshake between the Serb police commander and an EU official sent out a signal that the Kosovo Serb police officers are willing to work with the new mission.
Albanian apprehension
Meanwhile some ethnic Albanians are not happy with the way that it will operate, they believe that too many concessions have been made to Serbia.
A couple of protests were held in Pristina in the run up to the official launch.
Meanwhile some ethnic Albanians are not happy with the way that it will operate, they believe that too many concessions have been made to Serbia.
A couple of protests were held in Pristina in the run up to the official launch.
Outside the old UN headquarters there is graffiti that says "Eulex - Made in Serbia".
This mission is the biggest ever deployed by the EU.
This mission is the biggest ever deployed by the EU.
People from both sides want to see tangible results that improve their standard of living.
