In Classical Athens, the title was associated with the trierarchy (τριηραρχία, triērarchia), one of the public offices or liturgies, which were filled by wealthy citizens for a year.
As the name implies, the trierarch was responsible for the outfitting and crewing of a trireme, and for commanding it in battle.
Trierarchs thus had to be men of considerable means, since the expenses incurred could run as high as a talent in the course of a year.
As the cost of the office was great, co-trierarchs (syntriērarchoi) were also appointed.
By the 4th century BC, trierarchies in Athens were assumed by navy boards (symmoriai), as the financial burden of the job had become too great.