For certain combinations of protons and neutrons there is a theoretical expectation that the shape of nuclei can assume octupole deformation, which would give rise to reflection asymmetry or a “pear-shape” in the intrinsic frame, either dynamically (octupole vibrations) or statically (permanent octupole deformation). In this talk I will briefly review the historic evidence for reflection asymmetry in nuclei and describe how recent experiments carried out at REX-ISOLDE have constrained nuclear theory and how they contribute to tests of extensions of the Standard Model. I will also discuss future prospects for measuring nuclear shapes from Coulomb Excitation: experiments are being planned that will exploit beams from HIE-ISOLDE that are cooled in the TSR storage ring and injected into a solenoidal spectrometer similar to the HELIOS device developed at the Argonne National Laboratory.