Now in its 40th year, the 10-day festival has become a key launching pad for Hollywood's award season, with films like "12 Years a Slave", "The King's Speech" and "Slumdog Millionaire" all gaining critical momentum at the event before going on to win the Academy Award for best picture.
The festival started with the world premiere of "Demolition", starring Gyllenhaal and Naomi Watts.
Directed by Canadian Jean-Marc Vallee, it tells the story of an investment banker whose life unravels following the death of his wife. An unlikely connection with a vending machine company employee, played by Watts, helps him rebuild.
Vallee previously won praise for "Dallas Buyers Club" and "Wild".
Gyllenhaal said, to give the movie a realistic feel, the director allowed him to tear apart a house during one of his character's key scenes.
"It was incredibly cathartic. You feel like a kid," he told Reuters Television in a red carpet interview ahead of the premiere.
Thursday also saw the world premiere of Michael Moore's "Where to Invade Next", in which the "Fahrenheit 9/11" director looks at what former US President Dwight Eisenhower described as the military–industrial complex.