To begin with, his reign was spent fighting off Viking raiders, but in 904, at the Battle of Scones, he achieved a decisive victory and the Vikings were driven from the Scottish mainland. Thereafter his main concern was his southern border, with Saxon Northumbria, where the Vikings had resettled themselves, under Ragnall. Eventually, by 918, he had fought them to a standstill, in concert with Ealdred of Bernicia, and obtained the peace he needed.
It is believed that both groups of Vikings were of the Ui Imair ("descendants of Ivar) kindred who were then settled in Ireland and who are recorded as holding land there, on either side of the Irish Sea, and on either coast of Scotland, albeit in a local and fragmentary fashion rather than as an entire empire.
In 920 Constantine made a pact with the English king Edward the Elder, which he renewed in 927 with Edward's successor Athelstan. This was supposed to ensure their mutual neutrality so as to free up their attention to deal with the Viking threat.
However Constantine married, at unknown date, a daughter of the Norse king of Dublin, Olaf III Guthfrithson, and had at least 3 children. He therefore supported Olaf's claim to power in York around 934CE, which led to war. In 937 Athelstan won a victory, at Brunanburh, but on his death, and succession by Edmund, Olaf obtained York, while Vikings seized Northumbria, and Constantine benefitted by being insulated from the English kingdom's northward ambitions.
In 943, after an impressive reign, he abdicated in favour of his cousin Malcolm I, and retired to the monastery of St.Andrews, where he later became Abbot and died, in 952. His surviving son Indulf succeeded Malcolm on the throne.