This question was borrowed from a comment on this question. But what is meant by an "aggressive" climbing shoe? What is the difference in a non-aggressive shoe? And when would you use one over the other? Please use pics, I am a visual person.
Aggressive Climbing shoes are often also referred to as Cambered. The Arch of the foot and/or the toe point downward. Non-aggressive shoes have a flat bottom. Images compliments of rei.com.
Some people will use the term aggressive to mean tighter as well, but I have seen that to be less common. You want your shoes to be crazy tight, regardless of their shape. Also, the more aggressive the shoe, usually the longer break in period and the more painful.
This shoe is tilted but you can see the bottom is pretty flat. It is "non-aggressive"
This shoe is definitely not flat. It is "Aggressive"
So visually that is the difference. An aggressive show can have a down turned sole like the one in the pic or it could just have a down pointed toe.
Your Mileage may vary, but I have found the below to be true.
Flat Sole: The basis against which all others are judged. Not really bad at anything. Good for smearing.
Down turned Sole: Better for overhangs and roofs.
Flat Toe: Better for foot and toe jams.
Down pointed Toe: Good for Front pointing and Pocket Pulling as well as overhangs.