When It's Under Copyright: Fair Use
When Its License is not Covered By Copyright: Creative Commons Licenses and the Public Domain
For information on how to find images that are not under copyright ("Open images"), see Find Open Images on this guide.
You must always cite images appropriately
Most resources consider scholarly publication a commercial use and forbid it without special permissions.
However: A growing number of Museum & Art sources make an exception and allow free use of their images for scholarly books and journal articles:
See each site for information about limits and procedures.