When suspects are arrested or detained, they must be informed of their constitutional right against self-incrimination and the right to an attorney. If they are not told of their rights, any information gathered by police during an interrogation is inadmissible in a court of law. See, e.g. Miranda v. Arizona, 384 US 436 (1966). Subsequent lower court cases have ruled that statements given voluntarily are admissible even if Miranda rights were not read before the statement was given.
See also CRS Annotated Constitution: Fifth Amendment: Miranda v. Arizona