The latest row is over a gas exploration ship sent by Turkey to conduct research in a maritime zone Greece considers its own.

But the tug-of-war between the NATO allies for control of the Aegean goes back decades.

Here is a fact file on its origins:

- What is the source of the dispute? -

For decades, the historic rivals have maintained overlapping claims to the Aegean and eastern Mediterranean, and the suspected presence of rich hydrocarbon resources in the area has only heightened the dispute -- especially as close Greek ally Cyprus is also drawn in.

Turkey says that Greece unfairly regards the entire Aegean as a "Greek sea" in disregard of its own rights as a coastal state.

Athens says its only dispute with Ankara is over where to delimit the continental shelf -- the stretch of seabed close to its shores.

Exploratory talks have been held on and off on this issue since 2002.

But Turkey also questions postwar treaties that it says Greece is applying unfairly.

Greece currently adopts a six-nautical mile territorial sea and a 10-nautical mile airspace from its islands.

But it reserves the right under international law to extend its territorial rights to 12 nautical miles.

Athens notes this has been done by "virtually all coastal states in the international community, including Turkey" in the Black Sea and Eastern Mediterranean.

But Turkey has warned this would be a cause for war.

Turkey also accuses Greece of stationing troops on islands that were supposed to be demilitarised under the 1923 Treaty of Lausanne.

Athens counters that not only did Turkey invade and occupy the northern part of Cyprus in 1974, but that it maintains a "significant number of military units, aircraft and landing craft" just across from the Greek islands posing a "serious threat" against Greece.

- What is the legal background? -

The key documents in the dispute are the 1923 Treaty of Lausanne and the 1947 Treaty of Paris, under which Italy handed over to Greece the Dodecanese islands, which it had seized from Turkey in a 1911 war.

Turkey had no say in the 1947 treaty as it maintained neutrality during World War II.

Under the Treaty of Lausanne, Turkey ceded to Italy over a dozen islands including Kastellorizo, which lies just a couple of kilometres from the Turkish coast.

Turkish President Recep Tayyip Erdogan has repeatedly called the Treaty of Lausanne into question.

And Ankara says that unless specifically named in treaties, islets and rocks claimed by Greece are in fact 'grey zones' of unclear jurisdiction.

- Are tensions frequent? -

The closest Greece and Turkey came to war was in 1996 over Imia, a cluster of uninhabited islets known as Kardak in Turkey. That crisis was defused at the last minute by the Clinton administration in Washington.

Other major flare-ups involving Turkish exploration ships took place in 1976 and 1987.

The most habitual source of tension is flights by Turkish warplanes over Greek islands, which Greek jets are sent to intercept.

In 2006, a Greek pilot was killed when his plane collided with a Turkish jet during a mock dogfight in the Aegean.

Another died in 2018 en route to base after a similar mission.

- What other options exist? -

Greek Prime Minister Kyriakos Mitsotakis has expressed willingness to put the continental shelf dispute before the International Court of Justice at The Hague.

"We will respect the decision of the court," he recently told an online conference.

Marilena Koppa, an associate professor of comparative politics at Panteion University, warns that an ICJ hearing will likely lead to a "compromise", forcing both Greece and Turkey to abandon "maximalist" positions in the Aegean that prevailed for decades "mainly for domestic consumption."