Donald Glover's "Atlanta" was the top comedy nominee with 16 bids, poised to take advantage of this year's absence of three-time victor "Veep".
The category is completed by "Westworld", Netflix's "The Crown", which finished on 13 nominations, and the streaming service's sci-fi series "Stranger Things" (12), as well as NBC's family drama "This is Us".
Hulu's A Handmaid's Tale - which won the award for best drama series past year - earned 20 nods.
It was a very strong freshman class, and all five shows are back this year.
Markle's name was submitted for "Outstanding Supporting Actress in a Drama Series" for her role as Rachel Zane on "Suits", but the newly-minted royal wasn't nominated. With the nod - his seventh in a career that's spanned more than two decades - Dinklage becomes the most-nominated actor ever in the Emmys' best supporting actor category. Brown is also nominated for comedy series guest actor for "Brooklyn Nine-Nine".
"Among the welcome highlights, the Television Academy recognized the final season of "The Americans", Sandra Oh for her standout starring performance in BBC America's "Killing Eve", Issa Rae for HBO's "Insecure" and Ted Danson - representing one of the few major-network series to break through - for NBC's The Good Place".
Comedy show Saturday Night Live, which has been enjoying high ratings due to its focus on the Trump administration, was rewarded with 21 nominations.
The 70th Primetime Emmy Awards nominations are the culmination of a life's work and the goal of just about every television actor's career. And during Thursday's 2018 Emmy nominations announcement, it was revealed that it's been nominated for 22 more, including Best Drama Series, Best Directing for a Drama Series and Best Writing for a Drama Series.
"TBS bravely put a woman over 45 on TV and in turn I only got yelled at by the president once", she said in a statement.