This important book surveys recent progress in applying the most important quantum many-body techniques that have been developed to describe the properties of light-to-medium-mass atomic nuclei, from an initio microscopic approaching which only a knowledge of the basic forces between nucleons is assumed. Attention is focused on the relative advantages and disadvantages of each method, with the aim of identifying how the best elements of the most successful approaches may be combined. The different techniques are described and then brought into confrontation via their relative successes in describing the light nuclei. Key open issues are thereby identified, and suggestions for future work are outlined.