Swift is nominated for nine moonmen, including video of the year for "Bad Blood," starring Selena Gomez, Lena Dunham and more of the pop star's famous friends.
Lamar, who is featured on "Bad Blood," is nominated for video of the year thanks to his own hit, "Alright." Other nominees for the top prize include Beyonce's "7/11," Ed Sheeran's "Thinking out Loud" and "Uptown Funk" by Mark Ronson.
The 2015 VMAs, hosted by Miley Cyrus, will air live Aug. 30 from the Microsoft Theater in Los Angeles.
Swift's "Blank Space" will compete for best female video and pop video, while "Bad Blood" is up for best collaboration, direction, editing, visual effects, art direction and cinematography.
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Fans can begin voting today.
Beyonce, Sia, Nicki Minaj and Ellie Goulding will battle Swift for best female video, while Sheeran, Lamar, Ronson, the Weeknd and Nick Jonas will compete for best male video. Diplo, FKA twigs, Skrillex and Minaj earned three nominations each, while the Weeknd, Ariana Grande and Fetty Wap are double nominees.
Cyrus, who won video of the year last year for "Wrecking Ball," dominated the 2013 VMAs when she grinded on Robin Thicke during a performance that trended heavily on social media. Cyrus wrote in an Instagram post today that "MTV won't let me perform ... So I'm hosting this year's VMAs.