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Artworks and images are protected by copyright law, but Fair Use (section 107 of the U.S. Copyright Act) provides for certain cases where permission from the rights holder is not required. Detailed information about fair use and its four determining factors are available in the Using Copyrighted Works guide. Here are some resources to help you better understand it in the context of the visual arts:
A tool to help you better understand how to determine the "fairness" of a use under the U.S. Copyright Code.
Many images are made available via Creative Commons licenses, with various levels of use and remix restrictions. Detailed information about Creative Commons is available in the Using Copyrighted Works guide. These quick links cover the basics:
The Digital Image Rights Computator (DIRC) program is intended to assist the user in assessing the intellectual property status of a specific image documenting a work of art, a designed object, or a portion of the built environment. Understanding the presence or absence of rights in the various aspects of a given image will allow the user to make informed decisions regarding the intended educational uses of that image.
Artists Rights Society (ARS) is a copyright, licensing, and monitoring organization for visual artists in the United States that represents the intellectual property rights of over 50,000 international visual artists and their estates from around the world.