I've always had a fascination with precolumbian contact between the Afroeurasia and the Americas. There's the obvious ones with the Vikings and the descendants of modern day Inuit peoples, and the infamous (and unsubstantiated) claims of the Ming Dynasty fleet making it to the Americas, however the one I'm interested in with this question is the possibility of Polynesian contact.
When I last spent time reading about this subject it seemed to be that it was theoretically possible, but there was little to no positive evidence, thus making it more of an interesting possibility, but not much more than that. Has this changed? Do we have better evidence at this point? Or does is this theory still stuck in the space of interesting speculation, but not academic reality?
While there may be more to be said, you'll be interested in these responses from /u/reedstilt and /u/cozijo and this response from /u/b1uepenguin.
In short, there are several lines of evidence for which Polynesian arrival in the Americas is a parsimonious explanation. This recent article added some additional support. There is no evidence, however, for the actual contact event: neither region's material culture has been found across the ocean.