Relevant information from the Wikipedia page:
"Varangians" was in Byzantine service from as early as 874. The Guard was first formally constituted under Emperor Basil II in 988. People identified as Varangians were to be found in Constantinople around 1400.
Who?
The guard was primarily composed of Germanic peoples, specifically Scandinavians, and Anglo-Saxons (after the Norman Conquest of England created an Anglo-Saxon emigration).
Appearance:
The Varangians relied on a long axe as their main weapon, although they were often skilled swordsmen or archers as well. They have also been described as mounted.
11th-century Byzantine historian Michael Psellus: “The whole group carry shields and brandish on their shoulders a certain single-edged, heavy-iron weapon"
About the Guard: Role and reputation
The Varangians served as the personal bodyguards of the emperor. They had ceremonial duties as retainers and acclaimers, and performed some police duties.
The Guard was only used in battle during critical moments, or where the battle was most fierce.
Contemporary Byzantine chroniclers tells of a mix of terror and fascination for the Vikings:
"Scandinavians were frightening both in appearance and in equipment, they attacked with reckless rage and neither cared about losing blood nor their wounds".
(This description probably refers to 'berserkers', since this state of trance is said to have given them superhuman strength and no sense of pain from their wounds).
The Varangians had the unique right of running to the imperial treasury and taking as much gold and as many gems as they could carry, when the Byzantine Emperor died.
This privilege enabled many Varangians to return home as wealthy men, which encouraged even more Scandinavians to enlist in the Guard in Miklagarðr (Miklagard = 'The Great City', i.e. Constantinople).
The loyalty of the Varangians became a trope of Byzantine writers.
However, unlike the native Byzantine guards, the Varangian guards' loyalties lay with the position of Emperor, not the man that sat on the throne. This was made clear in 969 when the guards failed to avenge the death by assassination of Emperor Nikephoros II. A servant had managed to call for the guards while the Emperor was being attacked, but when they arrived he was dead. They immediately knelt before John Tzimiskes, Nikephoros' murderer and hailed him as Emperor. "Alive they would have defended him to the last breath: dead there was no point in avenging him. They had a new master now.
In History:
They were vital to the Byzantine victory under the emperor John II Komnenos at the Battle of Beroia in 1122.
They were prominent in the defense of Constantinople during the Fourth Crusade.
Fun Fact:
One of the famous runic inscriptions in Hagia Sophia, (or early 'graffiti') was probably carved by members of the Varangian Guard