Read a history book about Vikings (albeit from 1971, but I doubt much more was discovered since then), so here's some history facts (that might not be entirely true because of lack of evidence) related to the show:
Warning, includes spoiler of the previous and potentionally future episodes. Mind that the book focused more on how the average viking lived rather than big historical events.
As a general note, it seems that the Vikings TV series is trying to clump a lot of Viking history under Ragnar, from the beginning at the end of 8th century to (probably, we've yet to see how long it'll take for him to die) it's end around the end of 12th century:
- Supposedly the first attack by Vikings, just like in the show, was on a monastery in the year 793 (Lindisfarne, Northumbria), no records of Ragnar being included
- Early on they had no ways to tell where they were going on open sea other than wind, stars and such surroundings
- Most of the times they spared no one on these looting raids, you were either killed or taken as a slave
- The attack on Paris happened several times, the first time was in year 845, and the book said Ragnar was present. They burned down Paris then. The way they took Paris in the show (using the coffin as a trojan horse) was taken from another attack on a city called Luna (made by his son Björn Ironside). King Horik (king of Denmark) was still present at that time, and Ragnar handed a hefty sum of loot to him, out of which a large part was returned to Franks as a compensation for burning down some other city iirc. Ragnar was mentioned as being a naval commander then, so I'm assuming he was (still) a Jarl then.
- Rollo doesn't seem to have any big connections to Ragnar, the proof of this being that he was born quite a few years later. Apparently Rollos attack on Paris years later (886) resembles more the one depicted in the show (without the trojan coffin), the first one done by Ragnar was easier. The characters of Count Odo and Gizele were also present there. Just like in the show Rollo marries Gizele after being christened and is offered to become the ruler of Normandy (northern part of France), if he accepts being vassal to the western Frank king. There was not much fighting with other vikings after that. Rollo lived long and has passed on his rule to his son, and grandson and so forth all the way to the point when 'vikings' of Normandy invaded England with William the Conqueror, so british royalty basically has viking/dane origins.
- Ragnars sons Ivar (the boneless) and Ubbe are mentioned in one of the attacks on England, having then also called themselves sons of Ragnar, whether it was for real or not
- No mentions of travels to Iceland, Greenland and Vinland (North America) in the shows yet, hope they touch this subject as it's also interesting
- No mention of Floki, and it was believed that there weren't really specialized ship builders then (at least in the early ages), mostly it was common farmers that became shipbuilders and after warriors when going on these cruises
- England was mostly attacked by danes, Ireland by norwegians, the two clashed occasionally
- At one point pretty much the entire british isles were under viking rule
- Franks were easy to attack because they were seriously unprepared for viking attacks at first and later when their king Charles the Great (Charlemange) died and the country was split in three between his sons
- Vikings were (surprisingly, to me) very tolerant to christianity unlike Floki, a lot of them accepted christian god as just one more god in their repertoire of gods, one more deity to pray to for their own greater fortune (most of them cared only for their own good). A lot of Viking traders had to be baptized/converted to christianity to be allowed to trade with rest of Europe. Rest were converted en masse by their leader accepting the faith and imposing it on his people, again surprisingly without much resistance. Thus, they were sooner or later all converted and this might also be one of the reasons why the attacks stopped.
- Swords as weapons and chainmail were for richer folk, hand axes for normal people
- There is some evidence that so called 'berserkers' existed, filling themselves with toxic mushrooms with LSD-like effects before going all mad and barely clothed into combat. Apparently a lot these died without an actual wound, as one of the monks then wrote
- Christian monks were a bit more realiable source of information of that time as they wrote more and nordic writings/sagas of what happened were often exaggerated and with a mystical flavour
- Ragnars banner was two crows
- Going by how the last season ended, we should be around year 910 in the show
EDIT: added more
