With a court order or subpoena police can access an individuals' text messages that are at least 180 days old from the cell provider, states ProPublica. American citizens typically cannot be wire tapped by the authorities without a warrant from a judge.
In most cases, when text messages have been accessed via the provider, the owner is not be notified, explains AlterNet. The Electronic Communications Privacy Act, or ECPA, is what governs how and what the government can access, states ProPublica. This Act does not apply to accessing text messages on a physical phone. Police need a warrant to access messages or other data on the cell phone of an arrested individual.