In 2016 Italy introduced "Formazioni Sociali Specifiche" as a legal framework for same-sex couples, granting them nearly the same rights and responsibilities as married couples, except for stepchild adoption.
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Spouses of the same gender who are foreign nationals have the right to live in Italy

A foreign national in Italy who has a same-sex partner from abroad may qualify for a residence permit based on familial ties, provided the relationship has been legally recognized and documented.

The non-EU partner of an Italian citizen, regardless of their gender, is eligible to attain Italian citizenship.

Non-EU nationals who are in a legally registered civil partnership with an Italian citizen can apply for Italian Citizenship. If the person resides in Italy, the application can be made two years after marriage. For those living abroad, it can be three years after. To be eligible, applicants must show basic knowledge of Italian, up to B1 level of the CEFRL (Common European Framework of Reference for Languages). People with a long-term EU residence permit, those who meet the Integration Agreement conditions, or those who possess a qualification from a state school or state-recognized private school are exempt from this requirement.
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Marriages between members of the same gender that are conducted in foreign countries.
The Italian authorities will recognize the validity of civil unions/partnerships/marriages celebrated in other countries, so long as they have been legally recognized in the place of their celebration.

Relationships between members of the same gender
This term refers to the legal recognition of couples who live together and share a life, regardless of their gender. Same-sex domestic partnerships are the equivalent of marriage for people of the same gender.
Couples (same-sex and otherwise) who are in a marital-type relationship and cohabitate while providing financial and emotional support to one another can be classified as domestic partners. To make the relationship legally binding, one of the partners must submit a form to the Office for National Statistics where they want to be recognized. This document states that they are requesting to enter into a "Convivenza per vincoli affettivi", or a common law partnership. Unfortunately, domestic partners cannot receive a family permit or citizenship. However, certain conditions may enable the partner of an EU/Italian citizen to get a family permit.