Vikings are a part of our history, the impact they did around the world (especially in europe) was giant. They raided many coasts and its believed that they reached America far earlier than Colombo did. But how far did they actually went? And was Ragnar Lodbrok (one of the most famous characters of the vikings culture, and probable father of Ivar the Boneless, Ubba, Bjorn Ironside and Halfdan aka Hvitserk) real or just an inspiration for viking berserkers and raiders?
So, do you ask the more or less accurate (in a sense that the majority of specialists reach an agreement) geographical extension of the activity sphere of the Vikings (or the Scandinavians/ Norsemen during the 'Viking Ages' (ca. 800-1050)? The following are conventional summary of their current understanding.
The Norsemen (those who spoke Old Norse - Scandinavian languages) mainly expanded in three directions from Scandinavia during that period:
1: Westward Way
As for American continents and adjacent Isles, except very famous L'Anse aux Meadows (link to UNESCO World Heritage Site, including the satellite map of the location) in New Foundland, in Canadian Province of New Foundland and Labrador, the scholars has not identified any other Norse (Viking) settlement from the Viking Age (before Columbus). This site had been said to occupy at most within a one generation (ca. 30 years) around the end of the first millennium, and to have functioned as a kind of 'base camp' for further exploration. The site seemed to have abandoned then (almost certainly together with the plan of settling permanently in the new land), though one recent survey suggests the possible later sporatic visit of the Norsemen in the 11th century.
We don't know whether this site (L'Anse aux Meadows) itself was really famous or notorious Vinland where Leifr Eríksson found in the narrative of later Icelandic sagas. On the other hand, the sagas also mention other place names like Helluland and Markland, in addition to Vinland. Helluland is usually identified with Baffin Islands in Arctic Canada, and Markland could be Labrador Peninsula. Fragmentary sources suggest that medieval Norse settlers in Greenland sometimes took a visit in Markland (Labrador) at least until the middle of the 14th century, though we have little archaeological finds there (in Baffin Islands or Ellesmere Island near Greenland some Norse artifacts have been found).
2: Southward Way
There are some records of the Viking assaults in the middle to the late 9th century Italy. In short, some of them even apparently intruded in the Mediterranean region via Gibraltar, but the amount of the reliable sources are rather limited. On the other hand, Islamic chroniclers in Iberian Peninsula as well as some Christian writers mention their sporadic incursions, mainly in western and southern part of the peninsula, from the middle of the 9th to the beginning of the 11th century. Some of the 'Vikings' active there, however, might have come from their new colony, Normandy, not directly from their (old) homeland, Scandinavia. From late 11th century onward (beyond the end of the Viking Ages in general sense), Christianized Scandinavians also traveled via Iberian Peninsula/ Gibraltar now as pilgrims or crusaders, though some sagas narrate a small scale of skirmishes between them and local Islamic as well as Christian people.
3: Eastward Way
This is the least known sphere of the Vikings (Norsemen in the Viking Ages) in the public, but increasing number of new researches as well as overview works has just been published for this topic. Since the 8th century, some Scandinavians expanded eastwards along with various waterways (Eastern Baltic Sea - Daugava - Volga - Dniepr) across Russia. There were two ultimate destinations in this direction: The 1st is Constantinople in Eastern Mediterranean (or even Jerusalem for the Christianized Norsemen), and the 2nd is the Volga river and further in Caspian Sea region. Some Islamic authors from the late 9th century record the visit of Rus' in slave markets there.
The Norsemen mainly traded the fur in the arctic and slaves (from Western Europe? and Southern Baltic) with the wealth, especially silver coins from the East in these markets. In Central Asia and NW Afghanistan, new silver mines had been found in the 8th century, and the flood of the silver traveled from East to West, and they were exchanged with the slaves that the Vikings brought into the market in Volga region. One famous saga account tells the future ventures of the Vikings, led by Yngvar, to Serkland in the East. Some scholars identify this Serkland in the Caucasus (now Georgia), though not all the experts agree to this identification.
(4: Northward Way?)
As I mentioned before in this thread, one of the most (relatively) trustworthy first hand of the accounts of the Norsemen in the Viking Age is the narrative of a certain rich Norsemen from Northern Norway, not extant in 10th century Old English manuscript. His name is Ottar (rendered Ohthere in Old English), and this narrative mention his voyage into the Arctic Sea, possibly to the White Sea. He went to this far Arctic Norway first to trade the fur with the hunter gathering people there,the Sámi, (and possibly to engage in hunting by himself).
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As for the second part of OP's question, I wrote a not so easy answer in the following thread before: Vikings and Ragna Lothbrok and his 5 sons, how accurate is the History Channel show?
Summary of my previous post are:
Recommended Introductory Work(s):
References: