Golden Globes 2017: 'La La Land' breaks record
Streep's "Doubt" costar, Viola Davis, presented the award and praised the actress.
"You make me proud to be an artist," Davis said. "You make me feel that what I have in me, my body, my face, my age, is enough."
Streep got political in her speech, highlighting the diversity of the various actors there from around the world.
"Hollywood is crawling with outsiders and foreigners and if we kick them all out, you'll have nothing to watch but football and mixed martial arts, which are not arts," she said.
Without mentioning his name, the actress criticized President-elect Donald Trump for his behavior on the campaign trail -- and called on the press to hold him accountable.
"We need the principled press to hold power to account, to call them on the carpet for every outrage," she said.
Streep ended her speech with words of wisdom from her friend, the late Carrie Fisher: "Take your broken heart, make it into art."
The Globes paid tribute to Fisher and her mother Debbie Reynolds, with a video highlighting some of their most memorable film roles.
Reynolds died one day after Fisher in December.
Davis, who earlier in the night won for best supporting actress in a motion picture for "Fences," thanked her co-star and the film's director, Denzel Washington.
She also paid tribute to her father.
"He had a story, and it deserved to be told and August Wilson told it," Davis said.
Casey Affleck and Isabelle Huppert won best actor and actress in the motion picture drama categories for their work in "Manchester by the Sea" and "Elle," respectively.
"Moonlight" was honored as the best motion picture drama -- potentially boosting the coming-of-age film's chances for more success at next month's Academy Awards.
In the television categories, FX's "People v. O.J. Simpson: American Crime Story" won for best TV movie/limited series.
Sarah Paulson, who portrayed prosecutor Marcia Clark in the series, also picked up a statuette for her work on the show.
"The Night Manager" scored wins for best actor and supporting actress in a limited series for its stars Hugh Laurie and Olivia Colman.
History was made when Tracee Ellis Ross won for best actress in a musical or comedy TV series. She became the first black woman to win in that category since Debbie Allen won for "Fame" in 1983.
"This is for all of the women, women of color and colorful people whose stories, ideas, thoughts are not always considered worthy, valid and important," Ross said. "But I want you to know I see you. We see you."
Newbie "Atlanta" won for best TV comedy series.
The show's creator and star, Donald Glover also won for best actor in a TV comedy.
"This is incredible," Glover said after his show, which has a majority black cast, won. "I really just want to thank Atlanta and all the black folks in Atlanta. For real, just for being alive...and being amazing people."
"The Crown," the acclaimed Netflix series about Queen Elizabeth II, won for best TV drama, with star Claire Foy taking the prize for best actress in a drama.