it doesn't matter if the profile is asymmetrical, its the airflow that matters.
Consider the many uses of symmetric airfoil, such as the NACA 00xx or NACA 00xxx series. One famous plane that used them was the Boeing B-17 where both the root and the tip were symmetric. Also many helicopter rotor blade profiles are symmetric. the Convair F-102 and F-106 are examples of interceptors with symmetric airfoils.
All the 'curved' asymmetric surfaces of an airfoil indicate is a non-zero camber. This affects the airfoils angle of zero lift, which works in conjunction with the wings angle of incidence to give the angle of attack in level flight.
The tradition curved asymmetric profiles are generally crap in supersonic flight, hence the interest in wedge and diamond ( double wedge ) profiles. These allow a more favorable location of shock waves and lowered wave drag at speed.
Controls, such as ailerons, and flaps allow control by altering the camber line of the airfoil changing its lift characteristics. Fowler flaps also increase effective wing area.
Some of this is Greek.

Oop, hit the post button by mistake. Okay, for those of us without a degree in Aeronautics, like me: NACA xxxx is a convention for describing how a wing is shaped. The first X is camber - the degree to which the wing is asymmetric.
http://en.wikipedia.org/wiki/Camber_(aerodynamics)
The second X describes where on the wing the maximum camber occurs as a function of distance from the leading edge. Ergo a 00xx is a wing with no camber - top and bottom curve to exactly the same degree from front to back.
Positive asymmetry (top bigger than the bottom) provides lift, but there are apparently situations where a 0 camber wing works well. However, I'm not entirely clear if that 0 camber bit on a B-17 is for the entire wing or just the outer end of the wing, because the linked article mentioned something about using low or no camber at the outer tip of the wing to reduce the chance of a spin. Not being a B-17 engineer, I don't have a way of finding that out.
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