Studies of the behavior of nanoparticle chain aggregates (NCA) have shown properties similar to those of molecular polymers. Like polymer chains, NCA tend to gather up and become more compact when heated. Under tensile stress, folded chain segments pull out and the NCA elongates. When the tension is relaxed, the chains contract. The stretching of NCA may contribute to the ductility of compacts made from nanoparticles, a subject of current research interest. In a well established technological application, carbon black and pyrogenic silica NCA produce remarkable increases in elastic modulus and tensile strength when added to commercial rubber. This may be due to the mechanical interaction between the polymer chains and NCA. However, basic mechanisms of NCA elasticity differ from those of molecular polymers. The alignment of chain segments when the NCA are subjected to tension probably results from rotation and translation at grain boundaries between neighboring nanocrystals. The elastic properties depend on the van der Waals forces between segments of the chain that fold to minimize surface free energy. Under tension, these segments pull out, but tend to reform when the tension is relaxed. The processes that lead to NCA formation and control the strength of interparticle bonds are briefly reviewed.