Currently the EU lets citizens of many non EU countries visit visa free (within the Schengen area) for a three months (90 days) period within every six months (180 days) period without needing any visa or permit or esta style visa or anything like that. They can just turn up at the border and enter. This includes citizens of, USA, Canada, Australia, New Zealand, Japan, South Korea, Georgia, United Arab Emirates, most of the Central America and South America countries, etc etc etc. So it is quite likely that the EU may put the UK in to this same category and apply this same policy to us.