On the death of the first King of Saudi Arabia, Abdulaziz Ibn Saud in 1953, his son, Saud became King of Saudi Arabia. In 1964, he was forced to abdicate; the next King was his half-brother, Faisal. The succession of Kings continued to the next elder brother, or the next willing or able elder brother, based on the decision of the family of Ibn Saud, several times in the line of succession a brother was removed from the line for different reasons. For example, Faisal's successor would have been Muhammad, but he declined the offer and Muhammad's younger full-brother, Khalid became the successor to Faisal. The six Kings of Saudi Arabia since 1953 have been sons of the first King, Abdulaziz.

In 2006 a council was created to appoint a Crown Prince (successor) to the current King. According to the rules of the council, the King nominates 3 possible successors and the council names one from the list to become the Kings successor.

The number of surviving and able sons of Abdulaziz continues to shrink; the current King, Salman initially had his brother Muqrin named as his successor, but he was replaced four months after his appointment with the King's nephew, Muhammad bin Nayef, who in turn was replaced with the King's eldest son as Crown Prince, Mohammad in 2017. Marking the first time the succession of Saudi Kings may pass from father to son in more than 60 years.

More Info: en.wikipedia.org