Below is a list of the most common categories through which most people are eligible for Dual Citizenship but there may be other ways you can apply as well. There is no limit to the number of generations back you can go to apply, as long as your ancestor was born in Italy and emigrated after March 17, 1861, which is the date Italy became unified as a country.
Each category below mentions the fact that the immigrant ancestor was still an Italian citizen at the time their child was born in the US. You should understand this to mean that eligibility depends on if and when your Italian immigrant ancestor became a US citizen. If your Italian immigrant ancestor never became a US citizen, that’s great, you just have to prove that with documentation (or actually the lack thereof). If your Italian immigrant ancestor DID become a US citizen, it has to be AFTER July 1, 1912 and AFTER their child (the one you are descended from) was born in the US. If your immigrant ancestor became a US citizen before the birth of their child, then that child did not receive citizenship upon birth and therefore could not pass it on to any descendants.
For more information on the categories and ways in which you might be eligible, refer to the Citizenship page for the Consulate in whose district you live. To find your Consulate, follow this link, click through to your Consulate’s web page, click Passports and Services, then Citizenship (usually on the left). Be sure to also click Citizenship By Descent (Jure Sanguinis) to see all available information.