At the time of Rome's great expansion in the first century AD, there was an almost "American Great West" movement afoot, ambitious emperors like Claudius and equally ambitious generals like Agricola, and a spirit of adventure and extreme self-confidence. There were setbacks of course, such as the loss of Augustus's legions in the forests of Germany and the almost disastrous rebellion of Boudicca in Britain that could have ended the Roman presence there. The British resistance was squashed decisively and the province remained Roman for another three or four hundred years until the breakdown caused by the Germanic invasions of England (Britannia), France (Gaul), and even Rome itself. However, even at its height, the empire never accomplished the conquest and rule of the entirety of the British Isles, most notably what is now Scotland, and more inexplicably Ireland. The Romans knew about these places of course, and traded with them -- merchants ventured far beyond where the legions went: there are remains of such contact up in the Inverness area, for example. Agricola had also sent a fleet around the entire island of Great Britain to establish that it was in fact an island. The northwest highlands and Hebrides were desolate and really not worth bothering with, perhaps with less than a couple of thousand inhabitants living very precariously. But the 'lowlands' of Galloway and Lothian and the lands north of the Firth of Forth (Pictland) were definitely of interest to the empire-builders. Here, and in the fertile Orkneys, is where the natives developed the Broch, a round stone tower rather resembling a power-plant cooling chimney, apparently as a defense against Roman slavers who ranged up and down the coasts.
Tacitus, the historian, was with the general Agricola on his campaign to subjugate all of Britain, and so we have the name of the first-mentioned 'Scotsman' in history, one Calgacus, who is reported to have said "Britons are being sold into Roman slavery every day and it is we who are next on the list to be taken. When that happens, there will be nothing left that we can call our own... Even our bravery will count against us, for the imperialists dislike that sort of spirit in a subject people." [quoted from Ancient Scotland, by Stewart Ross] Agricola had started a methodical campaign in the classic Roman tradition, building roads and forts at day's march intervals. He got almost up to what is now Aberdeen. Calgacus kept withdrawing into the hills, but finally had a pitched battle at Mons Graupius, which was a famous victory for the Romans (they lost 400 men whereas the Picts lost 10,000 -- well, take that as a propaganda statement). Unfortunately for Rome, Agricola was recalled home for political reasons, and nothing went right after that. Guerrilla warfare in the highlands of Caledonia and the impossibilty of urbanizing the natives -- standard Roman policy -- resulted in a retreat down to the Forth/Clyde valley where an earthwork wall, the 'Antonine Wall', was built as a boundary. A few major forts, such as Inchtuthill and Ardoth remained in the Grampians. Without infrastructure, none of this lasted very long. And cost a lot of money, with no return, so quickly cut by the Roman Senate.
Lack of home support for this expansion of the empire gradually led to the abandonment of the whole Caledonian project. The emperor Hadrian finally put a stop to the enterprise with the construction of his famous wall across Northumbria (excuse me for using this name, which did not exist then, but it makes the description clearer). Even back then, there was a tribe called the Brigantes, from which our term "brigands" comes, who lived in that area, cattle rustlers, vendetta/feuders, and rednecks just as their descendants were, and a constant pain to the Romans. The wall went through the middle of their territory and was thus a sort of Berlin Wall, with pretty much the same purpose. It worked for a long time, but obviously not in the long run. Northern Britain remained Celtic throughout the Roman hegemony, no matter how romanized the southern areas became, and with the later intermingling of Picts (Caledonians), Scots (Ulster Irish originally), and Angles (from northern Germany) became the distinctively different area it still remains.