Under the First Amendment, “Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peacefully to assemble, and to petition the Government for a redress of grievances.” As the Supreme Court has explained, “If there is a bedrock principle underlying the First Amendment, it is that the government may not prohibit the expression of an idea simply because society finds the idea itself offensive or disagreeable.” (Texas v. Johnson)

Though the text of the First Amendment limits only Congress’ ability to abridge speech, the courts have interpreted the First Amendment as being applicable to any “state action” by officials at any level of government. Thus, the First Amendment pertains to regulations by the FCC, acts of Congress, and the local police department. Private organizations, such as private art galleries or colleges, in contrast, are not technically bound by the First Amendment.
“Speech” has been broadly defined by the courts to include not only verbal expression, but also visual art, music, theater, dance, and other expressive conduct and non-verbal forms of communication. However, First Amendment rights are not absolute, and have some exceptions. Unprotected speech includes:

Government suppression of otherwise legal speech can be justified only if the government can advance a compelling reason. For example, national security concerns might justify suppression of an article describing military strategy in wartime. More often, free speech cases involve claims that government regulations are vague or overly broad, or that the government is engaging in viewpoint discrimination – trying to suppress speech because of opposition to the message it conveys. As this website details, different forms of expression are protected to varying degrees, often depending on where the expression occurs, and whether the regulation is formulated or applied to affect the content or viewpoint of the speech in that forum.