What has been the impact of America on the 20th century world? What are the new challenges to be faced to in 21st century America? Historians...

To me, historians call it the American Century because the
United States was central to everything that happened in the century after WWI (and the
US even had a large part in that).

It was US might that was
key to deciding World War II.  The competition between the US and the USSR dominated the
world from the end of WWII up to around 1990.  After that, the US was the only
superpower for the rest of the century.

In addition, the US
was the economic powerhouse of the world after WWII.  The US economy boomed, and that
pulled economies like that of Japan and, later, South Korea, with
it.

So the US dominated the 20th century in terms of
military and economic power.