In the 1990s and 2000s England's away support had a significant element of organised football hooligans. The violence at France 98 and Euro 2000 featured a lot of convicted hooligans and various clubs joining together to go and fight foreigners and foreign police (with plastic chairs usually). Outside of major tournaments the most notable example of this was the riot in Dublin in 1995, which had the added factor of far right involvement - a big crossover between far-right groups and football hooligans of course. This was covered extensively at the time. In response to this the government started to put in place more stringent conditions on convicted hooligans - travel bans became commonplace and even if people weren't specifically banned convicted hooligans were often made to report to parole officers for routine appointments during international torunamenets, which meant that travelling could see you put back in prison for parole violations etc. This, added to the fact that the 2002 world cup wasn't easily travelable, resulted in a change in the character of England's travelling support. There wasn't any serious trouble at Euro 2004, which was a big contrast to earlier tournaments and the same was true for the world cup in Germany.
While this is obviously a good thing and progress the change hasn't made the England fans entirely benign. England away games are now more like lads holidays turned up to 11 and all that entails. In most tournaments you now see England fans acting like pissed arseholes, shouting obscentiies at locals rather than going out to deliberately get into fights or create trouble. It's better than before but still not very pleasant. The affect of this is that when Russian hooligans turned up to Euro 2016 in Marsielles expecting 90s style English hooligans they found themselves beating up drunk guys wearing bucket hats and cargo shorts.
Scotland fans are very different but I do think there's going to be a change in character for the travelling support - I don't think groups of 18, 19, 20 year olds are going to be singing doh a deer and mooning local policewomen the way things were in the 1980s and 90s.. I'd expect that there might be more trouble than there once might have been but I'm sure it'll be very low level and not serious. I would, as stated above, take a national disgrace, pitch invasions, pyro and ultraviolence in exchange for a win.