According to the Schengen regulations entry is not permitted to “those who are considered a threat to public policy, internal security, public health or the international relations of any of the Member State”. Also, entry is not permittted to “persons for whom an alert has been issued in the Schengen Information System for the purposes of refusing entry”
Travelers are not subject to criminal conviction checks at border and minor criminal offenses should not prevent entry into the Schengen Area, however each county has its own policies which may be stricter or more relaxed. Generally speaking, European countries are not so concerned with minor offenses committed outside the EU borders.
As far as Italy is concerned, to enter the country, foreign nationals must NOT:
Starting in 2021 the EU Travel Information and Authorisation System (ETIAS) will become a requirement for visa waiver nationals. Applicants will be required to answer some security questions regarding criminal activity and applications will be processed against existing EU databases (Eurodac, SIS and VIS etc.), future systems and relevant Interpol databases.
More information on ETIAS can be found here: https://www.mazzeschi.it/etias-your-european-travel-authorisation/
Giuditta Petreni has over 10 years of experience in assisting companies and business investors with relocation of managers and staff to Italy. Giuditta has extensive experience advising corporate and private clients on a full range of Italian immigration categories. She is fluent in Italian and English.