The Medici family, also known as the House of Medici, was a very important and powerful Florentine family that sponsored through the financial success of the banking institution they possessed, the advance in art and science for almost two centuries of many highly recognized icons in such disciplines (Such as Michelangelo and Leonardo Da Vinci).
The first key event involved on the Medici Family’s rise was the foundation of the Medici Bank in 1397. Although they were already a rich and somewhat powerful family, the foundation of the Medici bank gave them power outside Florence and throughout all Europe.
Another key event was when the Medici Bank fell to bankruptcy in 1494, causing a strong decline on the Medici Family’s power and influence on many European royal houses but, nonetheless, they still had some power such in Italy and France as in the catholic church.
This earn them many privileged positions for almost another two centuries, producing four popes for the catholic church and two queens for the kingdom of France (Catherine De Medici and Marie De Medici). You can consider each one of those events as key for their return to power and influence over Europe.