Model Airplanes
After the successful flight of the first man-carrying flight machine invented by the now famous Wright brothers, excitement about interest in aviation spread quickly. As early as the 1900s' Model Airplane builders were already in existence. Many of the models were powered by rubber bands, twining type with double stick fuselages. Note that in the early days of model flying, small petrol and compressed air engines were also being used. The materials used in the model construction were birch strips, veneer, spruce, piano wire or bamboo often with an oiled silk covering. 
Using balsa wood for the structure and tissue covering first appeared in the United States around the late 1920s. The wings, fuselage, vertical and horizontal stabilizers, propellers, engines, landing gears appeared at about the same time. The lightness of Balsa wood helped the early model airplanes to fly with some degree of control during flight.
Successful flight depends on proper design of the airplane, it’s dimensions, weight considerations and, most importantly, the aerodynamic design.
There is a saying that goes “a feather flies better than a brick”. So keep in mind that even with a model airplane that has a good design, weight and balance plays a major role in it’s ability to fly.
As regards balancing; a well-balanced airplane is controllable during flight. Usually the fulcrum or center of gravity is located a quarter of the way down the wing chord because this is normally the aerodynamic center, the neutral point of the plane.
Looking at a cross section of the wing, you will usually find a shape called an airfoil which basically consists of an upper and lower chamber leading and a trailing edge. When the airplane is flying, there are aerodynamic forces that interact with the wings and act as both vertical and horizontal stabilizers because the airplane is flying against the air commonly called relative wind. This will create a variance of pressure on the upper versus the lower chambers of the airfoil (or the wing itself) which generates that critical lift. The air passing over the lower chamber must have a higher pressure against the upper chamber in order to sustain flight. This creates a lower pressure on the upper chamber based on the Bernoulli's theorem, "as the velocity of air increases, pressure decreases" giving us flight.
Models airplanes use the same basic principles as their much larger counterparts and thus are able to take flight.