Reflection-asymmetric shapes in atomic nuclei

Can atomic nuclei be unstable with respect to deformations that break intrinsic parity? On the theoretical side calculations indicate the existence of stable octupole deformations. There is also vast supporting experimental evidence for the presence of very collective low-energy dipole and octupole modes. In this contribution, recent advances in the physics of nuclear reflection-asymmetric shapes are discussed in terms of underlying shell effects. Particular attention is given to the recently predicted octupole excitations at superdeformed shapes.