The term "frying oil" can be used to refer to an oil used in small amounts to sauté or pan-fry with, or in large amounts to deep-fry with.
To be considered a good frying oil, an oil must be able to withstand being heated to a range of 375 and 390 F (190 to 200 C) without starting to give off smoke. Really good oils for frying can withstand being heated even higher.
The American food researcher Harold McGee did some experiments in 2010, comparing using cheaper "utility" cooking oils (such as canola oil, soy oil, etc) with expensive extra-virgin olive oils for frying. He found that heating oils obliterated any special tastes they might have started off with because it frees up aromas in the oils and lets them escape into the air -- one of the reasons that heating can be one of the techniques used industrially to deodorize raw oils. Consequently, he concluded there's little advantage to using the more expensive oils for frying.
Oil will, however, take on the taste of what you fry in it.
Oil used for deep-frying is frequently stored for re-use. Filter your frying oil before storing it to extend its storage life. Allow to cool, then strain, then store in fridge in a sealed container. Some people don't refrigerate it, but refrigeration extends its storage life.
If you fry fish or onions a lot, you may wish to store that oil separately and label it.
When you re-use frying oil, be mindful that the "smoke point" -- the point at which it smokes -- will be lower than fresh, brand-new oil because of the food particles that will be in the oil even though you strained it. Topping up with fresh oil will extend the useful life of your frying oil.
When you go to re-use it, if there is ever any off-odour, pitch the oil and start fresh. It is time to ditch your oil when there is an odour or it looks thick and dark, even when heated.
When you dispose of it, don't pour it down the drain, as sooner or later it is going to cause expensive drain problems. And, for sure, don't dump it down the drain if you are on a septic tank. Instead, take a jar or tin out of your recycling bin, empty it in there, refrigerate to let it solidify, then bin it.
The pros and cons of various oils for frying are covered within the separate entries for each oil.
 Few oils seems to have the sturdiness of beef fat, which some fish and chip shops still use for frying. It has a smoke point of 480 F / 250 C and a very high flash point of 550 F / 290 C.
McGee, Harold. Is It Time for an Oil Change? New York Times. 17 November 2010.
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