The United States used many of the atolls in the Marshall Islands as nuclear testing grounds from 1946 until the late 1950s. These nuclear tests have done irreversible damage to many of the atolls, the local population, and the wildlife in the region from coral reefs to sea life and more.
Outside the nuclear tests, the Americans did little to alter the culture other than introduce new technologies. The people continued to essentially self-rule their islands through this time, but communication and infrastructure improved with new technology.
In 1979 the United States granted the Marshall Islands greater independence (although full independence wasn't gained until 1986). Since that time the political scene has been fairly peaceful and quiet. The greatest political splashes have come with the United States. The two nations work together in a free association (which puts the United States in control of the Marshall Islands' defense), while the United States continues to control Kwajalein Atoll via payments and has also given the government of the Marshall Islands money as compensation for past nuclear testing.
The other political debate has come in controlling the government. The iroij dominated the political scene until 1999 when elections began to actually represent the people. This change is a symbolic shift in the culture as well. For centuries the culture and people have lived in a very tribal society as local chiefs controlled the political, economic, and even social lives of the people as there were few to no complaints regarding this system. Perhaps due to outside influences, the people have been empowered as they have taken control over the political scene and the people no longer see the iroij as unquestionable leaders, although they continue to receive a great deal of respect.