I don't usually post on Saturdays, but this seems to merit it. In the wake of the death of King ‘Abdullah of Saudi Arabia, King Salman has moved to replace positions vacated by the succession, and in so doing he has also given us the first official indication of when the next generation of princes will see the throne. Admittedly, it was pretty much inevitably going to be after Crown Prince Muqrin, but now we know who it will likely be.
Upon his accession, Salman confirmed the former Deputy Crown Prince (a position created by ‘Abdullah) Prince Muqrin, as Crown Prince. Then he appointed to Muqrin's previous post of Deputy Crown Prince the Interior Minister, Prince Muhammad bin Nayef. Now second in line for the throne after Muqrin, Muhammad bin Nayef is the first member of the next generation to be officially in line for the throne.
For more than 60 years, since the death of the Kingdom's founder, King ‘Abd al-‘Azīz Al Sa‘ud in 1953, every king of Saudi Arabia (Sa‘ud, Feisal, Khalid, Fahd, ‘Abdullah, and now Salman), as well as Crown Prince Muqrin, has been a son of the Kingdom's founder, who had more than 40 sons. But Muqrin is the youngest son of King ‘Abd al-‘Azīz. (Not the last surviving son as some were passed over for various reasons.) Now, barring unforeseen changes, it is likely Muhammad bin Nayef, the man behind the Kingdom's counterterrorism efforts, will be the first grandson to succeed.
King Salman, who had been serving as Defense Minister as well as Crown Prince, has named his own son, Prince Muhammad bin Salman, to succeed him at the Defense Ministry. Muhammad bin Salman, who had been Chief of the Crown Prince's Court before the succession, will also be Chief of the Royal Court.
Inevitably, when a succession occurs, the Senior Princes have to reach an accommodation on which branches of the family take what posts. How exactly this is done is only roughly known; I've already noted that those who speak don't know and those who know don't speak. I would be very wary of interpretations like this one by David Hearst of "A Saudi Palace Coup" in which he sees the so-called Sudeiri branch of the family as reversing the will of King ‘Abdullah. The Sudeiris were never exactly out of power; Salman is doing what any new King does, making his own appointments, but no Saudi King acts completely independently of the other Senior Princes.