In the archaic period, the most significant military development was the adoption of hoplite warfare by the Greek states. This occurred in the early part of the seventh century BC. The panoply, or hoplite’s armour, began to appear in the eighth century, and the earliest known example comes from Argos in the late eighth century.
While the pieces which made up the panoply were all in use in Greece by the end of the eighth century, our first evidence for it being worn as a complete set of armour does not come until around 675 BC, where it is depicted on a Corinthian vase painting. The adoption of the phalanx tactics which would be used by hoplites in the Classical period does not appear to have taken place until the mid-seventh century before this point, the older style of combat in which spears were thrown at the enemy before closing quarters was still used.
In the naval sphere, the archaic period saw the development of the trireme in Greece. In the eighth century, Greek navies began to use ships with two banks of oars, and the three banked trireme seems to have become popular in the seventh century. Corinth was probably the first place in the Greek world to adopt the trireme in the mid seventh century BC. It was not until the mid-sixth century, however, that the trireme became the most popular design for Greek battleships, due to its expense. According to Thucydides, the period saw the first Greek naval battles; he dates the first to around 664 BC.
Source: Wikipedia
