Great question! Olive oil sits on a fine line between the two ends of the spectrum. Chemically, it only has one chance to bond with oxygen so it is a bit more stable but it's still able to oxidize. Best practices for olive oil are to purchase extra virgin olive oil in a dark glass bottle and store it in a cabinet out of the light. As far as cooking, it is generally best not to heat it or at least not at medium to high temperatures. Personally I have made the switch to sauteing vegetables in coconut oil just to be as safe as possible.
Hope this helps!