The company was made up of several different divisions, but their primary business was shipping. Around 32 BBY they were allied to the Trade Federation, but by 3 ABY they had formed very close ties to the Galactic Empire. They were also affiliated with Black Sun. Their business tactics matched their allies, as they were known to try to ruin their enemies by whatever means necessary. These means ranged from threats to planting contraband at enemy storage facilities to outright attacks, like at Harlequin Station.
By the time of the Battle of Hoth, and probably much earlier, the company was headed by K'Armyn Viraxo, and had developed a bitter rivalry with Twin Suns Transport Services.
The Viraxo family was determined to ruin Twin Suns Transport Services in order to increase their own profits and prestige, so they often harassed the Azzameen family in what were almost always unprovoked attacks. The Azzameens in turn fought to defend their interests. This feud would prove disastrous when the Galactic Empire discovered the Azzameen family's affiliation with the Alliance to Restore the Republic, and the Empire soon seized the family's assets and handed them over to the Viraxo.
Despite this setback, the Azzameens continued to defend their interests and caused major damage to Viraxo Industries through a series of coordinated strikes on their cargo facilities, which resulted in irreplaceable losses for the company. The Azzameens even tried to assassinate K'armyn Viraxo in one attack, but K'armyn cheated death as he had been forewarned of the attack on his personal yacht, which was destroyed by the Azzameens. This failure implied that the Viraxo may have had a number of spies within Twin Suns Transport Services.
The Viraxo also briefly acquired control of the Azzameen Home Base after the Empire allowed them to seize the family's assets. They later sold this base to a band of mercenaries who harassed the Bothans, prominent members of the Rebel Alliance. However, this facility was eventually recaptured by the Azzameens with help from their Rebel allies.