Short answers, pulled from the story.
Odoacer became the first King of Italy when his soldiers proclaimed him Rex following his deposition of the Roman Emperor Zeno. He ruled from 433 until his death on the 15th of March 493.
Theodoric the Great defeated Odoacer in 493 to establish a new dynasty that lasted until 552. His reign spanned from 454 to the 30th of August 526 before the final Ostrogothic king fell to Emperor Justinian in 553.
Otto I invaded Italy in 951 and claimed it as a constituent realm while subsequent emperors used the title Rex Italicorum until Henry II ruled from 1004 to 1024. Imperial control receded to Trent and South Tyrol until the empire dissolved in 1806 after Charles V stopped being crowned king of Italy after January 1556.
Napoleon Bonaparte established a client state called the Kingdom of Italy on the 17th of March 1805 while also serving as Emperor of the French. This kingdom existed only until the 11th of April 1814 when Napoleon was deposed by European powers.
People voted in a plebiscite to join Sardinia and form the Kingdom of Italy in 1861 with Victor Emmanuel II becoming the first king on the 17th of March 1861. The Papal States and Rome were annexed in 1870 completing the unification process that had taken decades to achieve.
The monarchy ended after World War II when an institutional referendum was held on the 2nd of June 1946. Voters chose to abolish the monarchy and establish the Italian Republic instead while Umberto II left the country on the 12th of June 1846 marking the formal end of royal rule.