The first thing that popped into my mind is the current situation with North Korea. North Korea is currently involved in tests of medium range missiles, and this directly impacts both South Korea and the US as a result of the Korean War of the early 1950s. The war was quasi-ended by an armistice in '53, but the division of the country has never been settled, since the vast political differences between North and South are as different as ever. The fear that missiles from N. Korea could reach America is a direct connection to the war in the '50s.
There are any number of other current events still connecting us to the 1950s. The second one which comes to mind quickly is the cause of a free Tibet. The entire issue revolves around the military seizure of Tibet in 1950. I'm sure with a little research you could discover many more. The fact that we still listen to rock and roll relates to the '50s; organ transplants began in 1950 and thousands are performed every year now; Queen Elizabeth II, crowned in 1953, is still Queen of England today; civil rights struggles still continue today, although segregation was declared unconstitutional in 1954. There's plenty more.