A major challenge that the US faced during these years was the challenge from the "culture wars" that grew out of the Vietnam Era.
During the Vietnam Era, a counterculture arose that challenged traditional American ways. This counterculture pushed against accepted ideas of sex roles, race relations, attitudes towards authority, and patriotism among other things. These changes continued in the 1970s.
As these changes occurred, they stirred up a backlash among traditional Americans. This led to the rise of the "New Right." It also led to a situation where American politics became much more divisive. Issues of race became much more important. So did issues such as abortion and women's rights. In the years following Vietnam, there were major conflicts about America's role in the world and about what it meant to be a loyal American.
This challenge is historically important because it continues to affect us to this day. Much of our current political strife comes about because of the "culture wars." We will see such conflicts discussed over and over again between now and the election in November.