The field theory of elementary particles has so far failed to predict the detailed form of the interaction between neutrons and protons (nucleons), but the nucleon-nucleon scattering experiments are now sufficiently complete that for most purposes the interaction may be taken as known. At the same time a wealth of data concerning energy levels, transition probabilities and so on is available for literally hundreds of nuclei. Such measurements reveal that nuclei have an extremely rich structure, with both single-particle and collective properties, illustrating almost every feature of a many-body system. It is the purpose of this talk to review the extent to which we are able to understand these properties on the basis of the known two-body interaction. It will be shown how some features may be understood quite readily while others still pose fascinating problems.