Low-energy Coulomb excitation is capable of providing unique information on static electromagnetic moments of short-lived excited nuclear states, including non-yrast states. The process selectively populates low-lying collective states and is therefore ideally suited to study phenomena such as shape coexistence and development of exotic deformation (triaxial or octupole shapes). Historically, these experiments were restricted to stable isotopes. However, the advent of new facilities providing intense beams of short-lived radioactive species has opened the possibility to apply this powerful technique to a much wider range of nuclei. We discuss the observables that can be measured in a Coulomb-excitation experiment, their relation to nuclear structure parameters with an emphasis on the nuclear shape, and present some recent examples of Coulomb-excitation studies that provided outcomes relevant for the Shell Model.