Description: The canonical approach seeks to define a quantum theory of gravity by applying the standard rules of quantum mechanics to the general theory of relativity as far as possible. Due to the structural features of the latter, the rules of quantization have to be generalized and the canonical programme encounters several conceptual and technical obstructions that are the subject of ongoing research (particularly in the field of Loop Quantum Gravity). I will introduce some of these issues through a rather general discussion of the structural features of quantization and the general theory of relativity from the physics point of view. I will attempt to illustrate one particular aspect of the so-called Problem of Time through the use of a simple model.