Triremes were ancient war galleys, originating with the Phoenicians and best known from the fleets of Ancient Greece. The trireme was an enhancement of the two-banked warships that had been in use; an outrigger above the gunwale, projecting laterally beyond it, to accomodate a third line of rowers, had been added. These were the dominant warship in the Mediterranean from around 700 to 300 BC, although there has been some debate about the actual date of its introduction. The uncertainty is due, in large part, to ambiguities in the few scattered mentions of triremes by ancient Greek writers, such as Herodotus and Thucydides, but is also a result of an issue surrounding the evolutionary development of the ship.
It is commonly accepted that the trireme was introduced by Aminocles of Corinth, in roughly 721 BC. However, we also know that triremes were not truly effectively used in naval combat until about 525 BC, when Polycrates of Samos was able to contribute 40 triremes for a joint invasion of Egypt. To suppose that no improvements were made to the design of the trireme - as the 40 ships contributed by Polycrates were still relatively primitive - when, in ten years, the Athenians were able to make sufficient improvements to the design to ensure their naval ascendancy for 60 years, is something of a stretch of the imagination. Some historians argue, then, that the introduction of the trireme did not take place until during the reign of Polycrates of Samos, as he was known to have a fleet of pentekonters at the beginning of his rule, and yet had switched to triremes by 525 BC. This would make the revolution of the design by the Athenians, then, much more likely.
Add to this the uncertainty over the terminology used in the ancient texts - essentially, there is no guarantee that when the ancient writers used the term "trieres" that they were, in fact, referring to the trireme, and not to just any "warship" - and the introduction date of 721 BC becomes quite questionable.
However, there are some reinforcements for the suggestion of the earlier introduction. Herodotus mentions that the Egyptian pharoah, Necho (610 - 595 BC), built triremes on the Nile, for service in the Mediterranean, and in the Red Sea for service in the Indian Ocean. That particular Pharoah had close ties with Greece, and especially with Corinth, where it is likely - if the Corinthians had indeed introduced the ship in 721 BC - he acquired the design.
Additionally, there is a fragment of Attic pottery, dated to between 735 and 710 BC, which seems to show a ship with three levels of oarsmen, although the third level is unmanned in the illustration. It is thought that the image represents an early example, or even a prototype, of a trireme, and the unmanned third level is explained, by proponents of the earlier introduction theory, as being quite natural, since the illustration is part of a relief depicting an evacuation, and oarsmen would surely have been in short supply.
It is still not certain which of the two theories is true, and much research is still being done into the questions which surround the introduction of the warship.
Naval combat, during the ascendancy of the trireme, took place mainly by ramming enemy vessels, which would typically break apart from the force of the collision. In order for this to work well, the boats need to be both fast and maneuverable, which means they ought to have a large number of rowers but still remain as thin and short as possible. Earlier on longboats of increasing length were employed, culminating in the pentekonter, with 50 oarsmen, which was about the practical size limit for that design. However, the Phoenicians managed to construct larger galleys by having several layers of oarsmen stacked on top of one another, first two (the fairly uncommon bireme) and then three (the trireme itself).
Triremes did not sit especially low in the water, and so were fairly prone to tipping, especially in rough weather. They were equipped with sails, which were taken down before battles, but cramped conditions made them unsuited for long-distance travel unless nearby friendly soil was present to camp upon each night, especially since they did not usually carry a supply of freshwater with them. Sometimes they and other galleys were used to haul cargo, but relatively stable roundships were more often employed.
The two main ramming tactics were attempting to catch the enemy in the flank, and attempting to glide along side it with the oars pulled in, thereby snapping the other boat's oars and leaving it demobilized. These required considerable skill to execute, and so rowers had to be specially trained. The Greeks usually recruited them from the poorer citizens who could not afford to serve in the army. An Athenian trireme typically had 170 oarsmen and 20 officers, plus 10 marines to repel men who might attempt to board while the trireme was approaching its opponent.
Triremes were expensive to build and maintain (on the order of a talent), which together with the need for specialized crew meant that only a very few of the powers at the time could afford large fleets. Most notable of these were the Phoenician cities, which provided a navy for Persia and her predecessors, and Athens. The engagement between the two at the Battle of Salamis, where the latter won thanks to superior positioning and maneuverability, is one of the most famous naval engagements of all time. Less famous but no less important was the Battle of Aegospotami, which sealed the defeat of the Athenian Empire by Sparta and her allies.
During the Hellenistic period, the trireme was largely supplanted by larger galleys, especially the quinquereme. The largest on record was a quadragintareme ("40-reme") of unclear construction, so the numbers must not refer to additional banks of oars and probably refer to the number of rowers per vertical section, with multiple men on an oar. This change was accompanied by an increased reliance on tactics like boarding and using warships as platforms for artillery.
Triremes and smaller vessels continued to be employed, however. Only the poorest states would use them as the core of their navy, but lightened versions were often used as auxiliaries, and were quite effective against the heavier ships thanks to their greater maneuverability. With the rise of Rome, the larger warships became unnecessary, and by imperial times the fleet had relatively few of them. Instead it was centered around triremes, very similar to those used by the Athenians, and even lighter Liburnians, which had only one or two banks of oars but were different in construction than earlier pentekonters and biremes. The latter would become the basis for the Byzantine dromon and other Medieval galleys.