It's the refusal of entry into Italy at the border or shortly after arrival, before a person is formally admitted. It applies to people without the right documents, or in specific situations defined by law.
It's different from expulsion: it happens at the entry stage, not after a period of stay. There are still strict rules to protect people who might be entitled to asylum or protection.
Even at the border, asylum requests must be heard. A respingimento that ignores an asylum request can be challenged in court.
Official source
Ministero dell'Interno
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