How did monkeys get to what is now Latin America?

The continents of South America and Africa were not touching when Primates were roaming the earth, so scratch that idea... Monkeys most likely didn't cross over the "Land Bridge" in Alaska, or there would have been monkeys all over North America, or at least fossils, so scratch that idea. THey couldn't have evolved independently and be so similar to monkeys in Africa, so scratch that idea. I think the current theory is they floated across the atlantic on logs. Sounds pretty realistic (not). If monkeys came across the atlantic many thousands of years ago humans were not able to?