While in 1395 other Italian states were hit by the Black Death, Savoy, like Florence, was an exception. Thus, the weight of Savoy (until then rather sitting at the fence of northern Italy) became greater.
In 1407, Maffeo Servitore, a cunning Florentine diplomat, saw the weakness of the divided Northern Italy and devised a plan. Meeting with the rulers of Savoy and Venice, all of Northern Italy except Genoa was divided into spheres of influences, which said three states were allowed to conquer. Otherwise, the big three were supposed to live in peace. Until the 1430s, this was what happened: The little city states of Northern Italy (which were near collapse after the difficult 14th century) were "mopped up". As a result, many Italians left their country (especially from Pisa and Milan), going to France and Aragon, and some other states too, spreading Italian art.
1430-35, Savoy invaded the republic of Genoa, annexing it. The duke treated the conquered city relatively well, though; he wanted to use it to become a power in the Mediterranean, too.
The first Swiss-Savoy War happened in 1541-44. The former won, got the control over Graubünden, Tessin and Veltlin.
The second Swiss-Savoy War took place 1627-32. At the beginning the Swiss were in advantage, but later the rebellion in the Triple Monarchy of England-Castille-Portugal gave France the opportunity to strike against the Swiss. In the peace of Turin, Savoy joined the Alliance des Alpes, becoming a French satellite. This would hurt them in the future: Since they had fought in the anti-French War at France's side against the new kingdom of Italy, they lost Genoa and Milan, being cut off from the sea.
1768, the country joined the first French Republican War. In this war, in the Battle of Aix-en-Provence (May 1769) "the blackest day for the house of Savoy" happened: Crown prince Filiberto was captured by the French, while his brother Filippo and their cousin (also named Filippo) died in battle. In the Peace of Brussels 1772, (core) Savoy and Nice were ceded to France, but the duke of Savoy already was broken. Now he fell gradually under the influence of king Gioacchino of Italy, who influenced Filiberto III in making a contract that Savoy would fall to Italy after his death, which would come in 1779.