Spectroscopy of superdeformed nuclear states opens up an exciting possibility to probe new properties of the nuclear mean field. In particular, the unusually deformed atomic nucleus can serve as a microscopic laboratory of quantum‐mechanical symmetries of a three dimensional harmonic oscillator. The classifications and coupling schemes characteristic of weakly deformed systems are expected to be modified in the superdeformed world. The ‘‘superdeformed’’ symmetries lead to new quantum numbers and new effective interactions that can be employed in microscopic calculations. New classification schemes can be directly related to certain geometrical properties of the nuclear shape.