They say the tech giant bought off competitors and used restrictive contracts to maintain a monopoly for its app store on Android phones.
The states say Google forced some apps to pay 30% commission on their sales.
They say that helped it generate enormous profit margins, and left consumers paying more.
The states want a refund for Play Store customers, and civil penalties for Google.
They say Google also intended to pay Samsung, whose rival app store posed the biggest threat, to stop competing.
The Silicon Valley firm has rejected the charges.
Google says the litigation is more about boosting a few major app developers who want preferential treatment.