Glover was born in San Francisco, the son of Carrie (Hunley) and James Glover. His parents, who worked as postal workers, were highly active in the National Association for the Advancement of Colored People (NAACP), working to advance equal rights. Glover's mother, daughter of a midwife, was born in Louisville, Georgia and graduated from Paine College in Augusta, Georgia. As an adolescent and a young adult, Glover suffered from epilepsy but has not suffered a seizure since age 35.

Glover was an early supporter of former North Carolina Senator John Edwards in the 2008 Democratic presidential primaries until Edwards' withdrawal, although some news reports indicated that he had endorsed Ohio Congressman Dennis Kucinich, whom he had endorsed in 2004. After Edwards dropped out, Glover then endorsed Barack Obama. In February 2016, Glover endorsed Vermont Senator Bernie Sanders for the Democratic presidential nomination.  Glover was an outspoken critic of George W. Bush, calling him a known racist. "Yes, he's racist. We all knew that. As Texas's governor, Bush led a penitentiary system that executed more people than all the other U.S. states together. And most of the people who died were Afro-Americans or Hispanics."  Glover's support of California Proposition 7 (2008) led him to use his voice in an automated phone call to generate support for the measure before the election.  On the foreign policy of the Obama administration, Glover said: "I think the Obama administration has followed the same playbook, to a large extent, almost verbatim, as the Bush administration. I don't see anything different... On the domestic side, look here: What's so clear is that this country from the outset is projecting the interests of wealth and property. Look at the bailout of Wall Street. Why not the bailout of Main Street? He may be just a different face, and that face may happen to be black, and if it were Hillary Clinton, it would happen to be a woman.... But what choices do they have within the structure?"  Glover wrote the foreword to Phyllis Bennis' book, Challenging Empire: How People, Governments, and the UN Defy US Power. Glover is also a member of the board of directors of the Center for Economic and Policy Research, a think tank led by economist Dean Baker.

Did the Obama administration respond?