The paper aims at exploring the mobility and migration processes affecting Europe, at pointing out the main motivations of mobility and migration, the results of mobility and migration and the issues raised by these processes. On one hand, mobility and migration greatly helps to enhance quality and contributes to creating innovation; on the other hand both these porcesses might pose problems on the level of the individual, of the community and of the society. Cultural diversity has traditionally been part of daily experience in Europe, but due to increased mobility and migration Europe is facing new challenges in the way of experiencing and handling multiculturalism. Mobility, migration and intensifying multiculturalism trigger new challenges of intercultural interactions and crosscultural communication.