Extraction of Virgin Olive Oil
The olives are graded for quality and size. The biggest generally go for processing into table olives. A green olive is simply one that has been harvested before it has fully ripened. Some Varieties lend themselves to specific applications;
Table Olives, Black: Mission, Calamata
Table Olives, Green: Manzanillo, Spanish Queen
Olive Oil: Frantoio, Leccino
Selection of olives for oil is critical to the oil's final quality; pitfalls include use of olives that
-are too ripe
-have been oxidising to long after harvest (ideally, should pressed almost immediately)
-are reject olives from table olive selection
Thereafter they are washed, crushed into a paste (including pips and skins), and centrifuged to separate the components (Oil, Water, and Sansa/Pomace/Spent Pulp). Although the expected yield of oil from unheated pulp is about 20%, this may be increased (and the quality compromised) by heating same. Conventionally the threshold above which one may call one's oil "Cold Pressed" is 35 degrees C.
Although the oil is normally filtered, there is a modern trend NOT to do so; an unfiltered oil contains waxes (mostly vitamin E) and is cloudy at room temperature. The vitamin E retards the deterioration of the oil.
Virgin Olive Oil
If olives had lain in the sun after harvesting for a full, unusually hot April (Southern Hemisphere) day, the FFA of same may be, say, 1.1% - still palatable but not out of the top drawer. The oil would be from the Virgin pressing, but would lose the "Extra" denomination. If the FFA exceeds 1.5% it may not be called "Virgin" oil. Oils with a FFA exceeding 1% are generally refined into....
Pure Olive Oil
These oils have a low FFA (about 0.1%) and some virgin oil is usually added back to augment their flavour! Expect to pay nearly an Extra Virgin price for "Pure" olive oil, because it has the favouable fat profile of olive oil but is less prone to rancidity on the shelf. Its stablity is favoured by manufacturers who wish to add the oil to foreign material like cured olives or infusions of herbs. The price of this by-product is further augmented because transport and processing infrastructures internationally are improving all the time - unprocessed olives don't lie around for long in the 21st century. Because of the small volumes of low grade olive oil input material available in South Africa, no refining of olive oil takes place here. We offer this oil in bulk to manufacturers.
Pomace Olive Oil (aka "Sansa")
Olive presses are unable to extract a residual 4% olive oil the olive pulp. A process of "hexane extraction" is able to chemically extract most of this oil, which is then refined. Used primarily to make soap. We offer this oil in bulk to manufacturers.

Regarding the country of origin of oils;
1) Our local oils (about 20% of our national requirement) are the best available
2) Producer countries retain their best oils for their own internal consumption; I tasted Costa d'Oro DOP in 2003 in Umbria and it was superb. Their exports are blends and low on polyphenol flavours.
3) All countries produce both good and poor oils; in the global village, origin is meaningless.
4) The Italian component in Berio, one of the largest Italian oil exporters, might reach "as little as 20%", and I would venture to suggest the same applies to other exporters. The balance comes largely from Spain, who in turn get a large chunk from Tunisia, and so on!
The Italians argue that they add value thru smart buying, blending, and marketing. After all, Belgian Chocolate, for which the raw material comes from the Ivory Coast, is a product of Belgium.