Smectite clays (e.g. montmorillonite), belonging to the structural family called 2:1 phyllosilicates, are the main choice for designing polymer nanocomposites due to their low cost and rich intercalation chemistry allowing them to be chemically modified (organoclays) and to improve the compatibility with the polymer matrix. These hybrid materials, normally called polymeric nanocomposites (PNC), represent a radical alternative to conventional polymer composites and have focused the attention of both academia and industry because of their unexpected properties, and their straightforward synthesis and processing. Such materials on the nanoscale level show significant improvements in mechanical properties, heat distortion temperatures, thermal stability, flame retardancy and enhanced barrier properties. The combination of enhanced properties, weight reduction, and low cost has led to interesting commercial applications such as automotive and packaging, among others. All this justifies the growing interest of both academia and industry in the development of these hybrid materials. In this paper we describe the most significant findings in the clay/polymer nanocomposites field considering three polymer families: elastomers, thermosets and polymers from natural resources or biopolymers.