An American U-2 spy plane, piloted by Francis Gary Powers, is shot down over Russia, causing a major diplomatic incident and John F. Kennedy defeats Richard Nixon in a closely-fought presidential race.
This was a very quite year in the space race, with both Russia and America still working on the technologies that they would use in the next few years.
However, this doesn't mean that nothing at all happened, with Russia launching 'Sputnik V' containing small animals in a similar way to the 1957 'Laika' spacecraft, and the USA conducting similar test flights in their country.
The year after:
The year before:
The small animal spaceflights that were conducted in this period weren't the first involving animals - this was a record that was in fact held by the USA from when they launched fruit flies into space in 1947!