Olive oil is a good oil for low carbers. I spend a good deal of time working in Europe and I have discovered that the olive oil in France, Belgium, and Italy is far superior than anything I have tasted in the U.S. I have also learned that olive oil can taste different depending on the type of olive grown and the region in which it was grown. In Europe, there is a science about olive oil that simply eludes most Americans. Certain types of olive oil go best with certain foods, such as salads or seafood. In the U.S., you can purchase true European olive oil from Oliviers & Co. We love this lemon infused olive oil on salmon. It is expensive, but adds a very good taste to fish in particular. You can buy the good stuff in the U.S. at a supermarket if it says "first cold press" on the label (I have even seen bottles with the label "first cold pressed" or "first cold pressing" even in Wal-Mart, though it is very pricey).
There are several designations for olive oil, and I will try to summarize them below.
The best olive oil is cold pressed (at no more than 82 degrees Fahrenheit). The olive and the pit are ground up into a paste, which is then pressed to produce the oil. This is what is known in Europe as "extra virgin olive oil," and is very tasty. Since the United States is not a member of the International Olive Oil Council, the label "Extra Virgin" is meaningless in the U.S. and the olive oil you purchase here may contain mixtures of any of the types of oils listed below. For the really good olive oil, make sure is says something like, "First cold pressing" on the label.
"Virgin oil" uses slightly more ripened olives and is a bit more acidic than extra virgin.
A by-product of olive oil is the mass of olive pulp and stones, called "pomace." The pomace can be industrially processed using heat and chemicals to extract even more oil, but it is not as tasty as the oil from the first cold pressing. "Olive pomace oil" is rather bland and is often used for baking or deep frying.
"Olive oil" is a mixture of virgin oil and pomace oil. It is only slightly more tasty than the pomace oil.
What we consume in the U.S. is usually not fit to lubricate my roller skates, but the first cold pressed olive oil is very, very tasty. If you haven't tried the good stuff, and are turned off by olive oil, you should try some from the first cold pressing. Drizzle the good stuff on a salad, along with a good balsamic vinegar, and you have a very delightful taste sensation.