According to a summary released by Barr, "[t]he investigation did not establish that members of the Trump Campaign conspired or coordinated with the Russian government in its election interference activities."
But Barr also quoted Mueller's report as saying "while this report does not conclude that the President committed a crime, it also does not exonerate him."
Barr promised to release the full report to the American public in April, along with color-coded redactions. Each color would explain why that information had been hidden.
The report will be released on Thursday.
What happened now?
According to a Fox News report from Wednesday, President Donald Trump's legal team is working on a rebuttal to the Mueller report, to defend against any accusations that Trump and his administration obstructed the investigation in any way.
"They assumed all along that there was going to be a finding of no collusion, so the rebuttal is about obstruction," Fox's unnamed source said. "They are preparing a rebuttal to presumed allegations which will be refuted."
Trump has long complained that Mueller's investigation is a "witch hunt" that was pushed by his political enemies.
Trump lawyer Rudy Giuliani confirmed on Tuesday that the White House would be issuing a response, but did not go into detail about what that response might cover.