Pre-Columbian contact is the belief that people from the old world, including Europe, Asia or Oceania, reached The Americas before Christopher Columbus, as either explorers, traders, or colonizers. This obviously excludes the Indigenous People of the Americas ("Indians"). The concept of Pre-Columbian contact is in contrast to what was the orthodox theory, which is that proto-Indians moved over the Bering Land Bridge more than 10,000 years ago, and then spread throughout the Americas and developed in complete isolation until 1492.
The range of theories of Pre-Columbian contact is wide in both topic matter and academic rigor and acceptance. One piece of Pre-Columbian contact, that Norse explorers had a colony in Newfoundland in the 11th century, has been supported by incontrovertible evidence. Several other theories are controversial, but at least are proposed as scientific hypothesis. Then there are theories based on pseudo-scientific comparisons of indigenous American artifacts with old world artifacts, or that involve things that are improbable given the available archaeological and historical records. And then there are the myths: lost continents and alien intervention. It is hard, at first, when sorting through the theories, to tell exactly where it sits on the continuum.
And when someone stats wading into all the scientific and historical debate about the possibility of Pre-Columbian contact, a lot of different disciplines are involved, and the information is usually very technical, and hard to put into a holistic picture. For example, one of the key questions to whether Polynesian people could have reached North America is just how quickly they spread across the Pacific. And experts on boats, language divergence and genetic mutation rates will all have different, very technical answers on when this happened, which is why (apparently) the estimate of when humans arrived in Hawaii can differ by hundreds, or even a thousand years. There is not a single omnidisciplinary scientist who can give a definitive, "scientific" answer to questions like these. And there are dozens of different questions, ranging over thousands of years and dozens of civilizations, about whether the Chinese, Japanese, Polynesians, Celts, Romans, Phoenicians, etc. would have had the technology or interest to reach the Americas.
My own believe, on balance, is that I think that the more fanciful theories of transoceanic contact are not true. For example, if Egyptians had the ability to regularly go to Central America and direct the building of pyramids, how could this have never happened to have been mentioned in any Egyptian, Greek or Roman records? But on the other hand, we do know that for hundreds and thousands of years, cultures with strong maritime abilities were sailing the Atlantic and Pacific. We know that Vikings made the trip to North America across the cold northern Atlantic in open boats. Is it totally impossible to believe a Roman or Japanese ship, maybe blown off course, maybe a fleeing pirate, could have landed in the Americas? Or for that matter, if we believe that groups of people over 10,000 years ago, living in the ice age climate of Beringia, could have expanded southward through the inhospitable and glaciated terrain of Alaska and Northern Canada, that nobody else afterwards could have made the same journey? For me, the burden of proof for incidental contact is not "how could it have happened", but "how could it not have happened".