The structural properties of free nanoclusters are reviewed. Special attention is paid to the interplay of energetic, thermodynamic and kinetic factors in the explanation of the clusters structures which are actually observed in the experiments. The review starts with a brief summary of the experimental methods for the production of free nanoclusters, and then proceeds with a guideline given by theoretical and simulation issues, always discussed in close connection with the experimental results. The energetic properties are treated first, evidencing general trends, describing the methods for modelling the interactions between the elementary cluster constituents, and for the global optimization on the cluster potential energy surface. After that, a chapter on cluster thermodynamics follows. The discussion includes the analysis of solid-solid structural transitions, and of melting with its size dependence. The last part is devoted to the growth kinetics of free nanoclusters, and treats the growth of isolated clusters and their coalescence. Several specific systems are analyzed.