Under the Italian law, citizenship is passed from a parent to the child according to the jure sanguinis principle.
Jus sanguinis (right of blood) is a principle by which citizenship is not determined by the place of birth but by having one or both parents who are citizens of the state. This principle contrasts with ius soli (Latin: right of soil) which is used by most countries in North and South America.
As a consequence, an individual is Italian if at least one of the parent is, regardless the place of birth. Citizenship is passed on from parent to child without limitation of generation, on the condition that none of the ascendants has ever renounced their citizenship.
When a person claims to be of Italian parentage or ancestry it is necessary to submit proof of the fact that the Italian immigrant (also known as Italian ancestor) maintained Italian citizenship until the birth of the first intermediate ascendant. That is the main condition that must apply in order for all descendants to qualify for citizenship.
Transmission of citizenship through maternal lineage is possible only for persons born after January 1st 1948. In other words, although the woman was an Italian citizen at the time of the child’s birth, the child could not inherit Italian citizenship from the mother if the the child was born prior to 1948.
This rule is enforced by all consulates but it has been overruled by Italian courts.