The traditional definition of a desert is an area that has below a certain level of rainfall, but I say that definition isnt clear enough.
While most of Antarctica is cold and frozen (considered a desert continent), beneath the snow, it looks barren like a desert (McMurdo valley photos are the perfect example of this.). Many sources classify tundra as desert because of low rainfall, but that doesnt make that much sense either.
Low rainfall of tundra doesnt make the vegetation look barren like in Arizona. Tundras are full of green grass and moss-they are far more moist than the ground and vegetation of most low rainfall areas.. Because of that, some scientific sources classify tundra as seperate from desert, because of how the amount of low rainfall effecting its vegetation differs from how low rainfall affects vegitation in other areas. Amount of rainfall that affects vegetation depends on temperature, and tundra is very cold.
Another example is-the Okanagan region of Canada, while being dry, has far more lush vegitation than a desert, but some consider it to be a desert because of its low rainfall, despite simply being shrub steppe.http://en.wikipedia.org/wiki/Shrub-steppe
Also, there are certain areas that dont have low rainfall, but the rainfall affects soil moisture and vegitation in ways very similar to a desert, like the Highlands of Iceland (http://en.wikipedia.org/wiki/Highlands_of_Iceland), and the Kau Desert of Hawaii (http://en.wikipedia.org/wiki/Ka%CA%BB%C5%AB_Desert). Do you think those regions fit the definition of a desert?
Other areas in which there is low rainfall and a desertlike appearence, some dont classify them as being "true deserts" because they dont fall under a certain level of rainfall. Examples of this would include regions in Spain and Washington State, like the Tabernas region of Spain, and the Channeled Scrublands of Eastern WA.