Children from 0 to 3 years old travel for free and don't need a ticket.
On high-speed trains (Frecciarossa and Frecciargento), Intercity, Intercity Night, Leonardo express (Rome - Fiumicino Airport) children are considered from 4 to 14 years old. Child fare applies and they need a ticket.
On regional trains, children are considered from 4 to 11 years old. Child fare applies and they need a ticket.
Bimbi Gratis fare: allows children under the age of 15 to travel for free when accompanied by a family/group of 2-5 people (with at least one adult and one child under the age of 15).

On Thalys (Belgium-Germany-France-the Netherlands) trains, children from 0 to 3 years old travel free and don't need a ticket.
Children fare applies from 4 to 11 years old and they need a ticket.
Youth fare applies from 12 to 25 years old and they need a ticket.
On Euronight Italy-Austria and Italy-Germany trains, children from 0 to 5 years old travel free and don't need a ticket.
Children fare applies from 6 to 14 years old and they need a ticket.
On Italy-Switzerland trains, children from 0 to 5 years old travel free and don't need a ticket.
Children fare applies from 6 to 15 years old and they need a ticket.
On Italy-France trains, children from 0 to 3 years old travel free and don't need a ticket.
Children fare applies from 4 to 11 years old and they need a ticket.