Let's start off with a basic one that just seems like a glaring oversight, shall we?
Paul Thomas Anderson is one of the best modern directors we have. From his earlier days with films like Boogie Nights to his most recent work in Phantom Thread, the man delivers some truly wonderful films that utilize the craft to cut to the bone.
He makes quiet and intimate films that feature great performances and a tangible aesthetics, that are also delightfully strange. For crying out loud, Phantom Thread is about a man who needs to be poisoned in order to feel receptive to love and ends with said man chowing down on an omelet he knows to be poison... and that's a happy ending.
He's also an Oscar favorite, in theory. His films are constantly receiving critical acclaim and getting nominated by the Oscars, but he has never actually won Best Director.