As of 16 February 2007 the EU Long Term Residence Permit replaced the permit previously known as the Carta di Soggiorno.
Further information is provided in English on the website of the Polizia di Stato:
The requirements for an EU Long Term residence application are that the applicant has resided in Italy for a period of at least 5 years, their income is sufficient to financially support themselves and their family unit and the applicant has not been accused of any crime for which he/she could have been arrested or charged and he/she is not awaiting trial or sentencing.
As of 9 December 2010 an additional requirement of knowledge of the Italian language has now been enforced. It is compulsory that applicants for this Permit pass the equivalent to the A2 level standard approved by the Council of Europe.
It is possible to add family members to your application as long as you are able to demonstrate that they too have resided in Italy for a minimum of 5 years and that accommodation is available to them without being a burden on the State.
We are able to assist you in gathering relevant documentation, obtaining translations of various documents and certifications known as ‘apostilles’ and making legal representations in support of your EU long-term residence application. These applications will then be submitted to one of the following bodies: Post Office (uffici postali), Municipal Office (comune) or Authorized Offices (patronati).
Benefits include entering Italy without the need of a visa, permission to work and access to social benefits and social services supplied by the Italian government.
n.b. Applicants who wish to: apply for study or professional reasons, remain in Italy on a short-term basis or diplomats/consulates belonging to international organs are not eligible to apply for this Permit.