The Romans established a naval base in (what is now) Brindisi (at the heel) in 246 BCE, partially to block Carthaginian ships from entering the Adriatic, and partially to deal with the Illyrians. Illyrians inhabited the eastern side of the Sea and acted as pirates to traders. Rome and Illyria fought on and off from 229-168 BCE.
After the decline of Rome, the coasts were ruled by the Byzantine Empire under Justinian, the Lombards, and the Ostrogoths. A few centuries later, with the rise of the Carolingians, the Frankish Kingdom of Italy controlled the western coasts and the Byzantines kept control of the eastern. It was around this time (700) that the Republic of Venice was founded. They thrived early on because of the salt trade, eventually developing a thalassocracy, a maritime empire known more for its presence on the sea than for possession of land.
In 999 CE, the Normans conquered southern Italy, eventually establishing the Kingdom of Sicily. Against this growing power, Alexios I of Constantinople issued a Golden Bull to Venice, offering them tax-free trading with the Byzantine Empire if their navy would control the spread of Normans.
The Adriatic was controlled by the Republic of Venice for centuries after that, and we will look at the Republic a little closer tomorrow.