High-resolution laser spectroscopy is an established powerful tool in the study of nuclear shape, size and multipole moments. Measurements of the hyperfine structures and isotope shifts in the atomic spectra of radioactive nuclei provide unique insight into the evolution of the nuclear macroscopic shape and microscopic structure. These measurements can be made with high precision and high sensitivity and applied directly on-line at radioactive nuclear beam facilities. Recent measurements, advances at facilities and the future direction of the field are reviewed. A summary of experimental data is presented.