The properties of semiconducting oxide heterostructures are demonstrated using ZnO and its ternary alloy MgxZn1 − xO as a model system. This system is of particular importance, as it shows by far the most detailed research activities among oxide semiconductors. MgxZn1 − xO can be grown pseudomorphically on single crystalline ZnO in the step flow growth mode yielding atomically flat surfaces. In such structures, a two-dimensional electron gas was detected with an areal concentration of up to n2d = 3.9 × 1013 cm−2. The quantum Hall effect was observed in ZnO/MgxZn1 − xO single heterostructures, the first oxide system ever to show the quantum Hall effect. Likewise, quantization plays a dominating role in double heterostructures of ZnO and MgxZn1 − xO. Quantum confinement and the quantum-confined Stark effect were observed in ZnO/MgxZn1 − xO quantum wells grown by MBE and also by PLD. Finally, the ability to induce and control quantized states in ZnO/MgxZn1 − xO heterostructures was combined with the extraordinary properties of one-dimensional nanostructures, thus resulting in nano-sized building blocks.