  A quantitative analysis of the evolution of nuclear shapes and shape phase
transitions, including regions of short-lived nuclei that are becoming
accessible in experiments at radioactive-beam facilities, necessitate accurate
modeling of the underlying nucleonic dynamics. Important theoretical advances
have recently been made in studies of complex shapes and the corresponding
excitation spectra and electromagnetic decay patterns, especially in the
"beyond mean-field" framework based on nuclear density functionals. Interesting
applications include studies of shape evolution and coexistence in N = 28
isotones, the structure of lowest $0^+$ excitations in deformed N $\approx$ 90
rare-earth nuclei, and quadrupole and octupole shape transitions in thorium
isotopes.
