Globalization has increased contact between peoples as never before. Migration flows are strong and more and more growing. This phenomenon has led to social conflicts. A possible solution could come from the ‘dialogue’ among courts of different States. The dialogue among courts has developed by means the circulation of interpretations of constitutional law concerning fundamental rights. Such a dialogue can close the gap between different levels of protection of fundamental rights. Western states share common constitutional principles. These principles converge in a ‘constitutional common core’ from which the courts can draw on to interpret the constitutional text in a reasonably uniform way. The presence of the guest citizen can excite this dialogue. The guest citizen may ask the courts of the host State to adopt the most advanced solutions in interpreting fundamental rights. The outcome of this dialogue is the ‘cosmopolitan constitutional law’: a new challenge to deal with problems of globalization.