Events at the Republican National Convention, being held this week in Cleveland, have made some people curious about copyright, plagiarism, and whether or not musical artists have complete control over who can and cannot use their music. One place to start researching these topics is at the U.S. Copyright Office, which is part of the Library of Congress:
Other places worth checking are the sites of the Copyright Clearance Center, the American Society of Composers, Authors, and Publishers (ASCAP), and BMI. For really complicated questions you can consult a lawyer who specializes in copyright (but I'm not sure even they understand it completely).