"This has been a time of great personal and professional transition for each of us," they said in a joint statement. "After a great deal of thought, reflection, discussion, and prayer, we came to this decision together. At this time, we are living apart, while we work on the future of our relationship.
"We are continuing to parent our four children together. They are the light and the center of both of our lives. We consider this a private matter, and neither we nor any of our friends or family will have further comment. We ask for compassion and respect from the media and the public."
From the beginning, they were an unlikely pair- the Republican movie star and the daughter of iconic Democrats.
Schwarzenegger, former governor of California, and Shriver, an author and former TV reporter, have been married for 25 years. They have four children and had been living at a private estate in Brentwood, Calif.
Schwarzenegger finished his seven-year run as governor in January.