The Antiquities Act allows “the President to set aside and reserve for use as public parks or reserves and public lands upon which are monuments, cliff-dwellings, cemeteries, graves, mounds, forts, or any other work of prehistoric, primitive, or aboriginal man, and also any natural formation of scientific or scenic or scenic value or interest, or natural wonder or curiosity together with such addition area of land surrounding or adjoining the same, as he may deem necessary for the proper preservation and subsequent investigation of said prehistoric work or remains.”
National Monument managers include the National Park Service, the US Forest Service, the Bureau of Land Management, and the National Oceanic and Atmospheric Administration.
There have been 124 monuments created through the act; some of these have later been designated National Parks/Preserves through the action of Congress. You can find a list of the monuments with the President who dedicated them at this link.
The first was Devil’s Tower in Wyoming, dedicated by Theodore Roosevelt in 1906 shortly after The Antiquities Act was signed into law. The latest was the Organ Mountains – Desert Peaks in New Mexico in May of this year by Barack Obama.