Here are some answers to key questions about the case:
WHAT ARE THE ALLEGATIONS AGAINST GOOGLE?
The Justice Department alleges that Google broke antitrust law to maintain its monopoly in search, where it has about 90 percent of the U.S. market, and two kinds of advertising - search advertising and general search text advertising.
As evidence, the department points to billions of dollars that Google pays to smartphone makers such as Apple, Samsung and others to make Google's search engine the default on their devices. As a result, the government argued, smaller search engines never get the scale they need to improve their algorithms, and grow.
WHAT REMEDIES DID THE JUSTICE DEPARTMENT REQUEST THE JUDGE IMPOSE?
The Justice Department has broad leeway in requesting a remedy and on Tuesday, it said "nothing was off the table," including a breakup of the search and advertising company.
In the complaint's "request for relief," the U.S. is seeking "structural relief as needed to cure any anti-competitive harm." "Structural relief" in antitrust matters generally means the sale of an asset.
It also asked the court to order Google to stop anti-competitive behavior and to pay the government's costs.
WHAT OTHER ALLEGATIONS HAVE BEEN MADE AGAINST GOOGLE?
In the past, Google has been accused of using its popular search function to favor its products, like YouTube, as well as big advertisers.
For example, a recent search for a "Saturday Night Live" video resulted in several choices from Google's YouTube before NBC, which produces the show. Companies such as Yelp have argued they are better than Google at helping consumers find certain services but that they often appear below a box of Google recommendations, resulting in fewer clicks.
Other allegations relate to advertising more broadly. In advertising, Google dominates the interlocking businesses that connect advertisers with newspapers, websites and other firms looking to host them. Google has been accused of being opaque in revealing its revenue from transactions, using "bundles" of products to disadvantage smaller rivals, and of rigging auctions.
WHAT DOES GOOGLE SAY ABOUT THESE ALLEGATIONS?
Google on Tuesday called the lawsuit against the company "deeply flawed" and said that users would find it more difficult to access superior search tools and affordable smartphones if the government wins its case.
Regarding search, Google has said that users have access to other information sources, like Twitter for news and Amazon for products. And it says that people use Google for quick answers, which has spurred the company to develop new ways to organize results.
In terms of advertising, it argues that it competes with a large array of companies, including giants like Oracle Corp and Verizon Communications Inc. And it argues that online advertising prices have steadily declined over the past decade.
As for Android, Google has said that phone makers that use its smartphone system do not have to include Google apps and may pre-install competing apps.
WHAT ROLE DO STATE ATTORNEYS GENERAL HAVE?
A large group of attorneys general is also investigating Google, with 11 states joining the DOJ suit Tuesday. A group headed by Texas is focused on Google's advertising practices, while other states are looking at search and Android. These may also result in lawsuits.
HOW LONG WOULD A TRIAL AND APPEALS TAKE?
It is in Google's interest to drag out the legal fight. Antitrust experts say it would take at least six to nine months to get to trial, with a decision coming several months after the trial's end. It would then likely be appealed.
On Tuesday, Google said it typically takes 12 to 18 months before such cases get to trial.
ARE THE ALLEGATIONS AGAINST GOOGLE POLITICALLY MOTIVATED?
Several tech trade lobbying groups said the suit was politically motivated. "The suit was hurried out on the eve of an election where the administration has aggressively pressured tech companies to take actions in its favor," the Computer & Communications Industry Association said in a statement.
President Donald Trump's administration has been angry with several Silicon Valley companies for allegedly silencing conservatives and many Republican lawmakers have brought up the issue of bias during recent antitrust congressional hearings.
(Reporting by Diane Bartz and Nandita Bose in Washington; Editing by Edward Tobin)