Triremes were the dreadnoughts of the classical era. They were expensive and required a great deal of maritime expertise, not to mention social class cohesion, in order to be effective in battle. The Athenian democratic political structure led to Athens dominating the seas until losses in the latter part of the Peloponessian War meant a degradation of the quantitative and qualitative advantages they held over the Spartans.

Trireme from didactylos47's photostream

Equally important was the logistical structure supporting the triremes. This is true for most military endeavours; American hegemony currently is based upon American dominance of logistics such that their forces can maintain a high tempo indefinitely. This was also true of the British military in their hay day. Triremes were short range weapons heavily reliant on human labor at the oars. Consequently they needed constant water and food provisioning. (more)
Cam Riley: South Sea Republic. Freedom, liberty, equity and an Australian Republic.