Polymeric materials having a plurality of cells formed therein are described. The polymeric materials include a foamed layer comprising a plurality of uniform microcells, nanocells or combinations thereof in a closed cell network, a transition layer positioned adjacent to the foamed layer, and at least one unfoamed outer layer positioned adjacent to the transition layer. The foamed layer may be present in a volume ranging from about 80 to about 99 percent based on the volume of the polymeric material, the transition layer may present in a volume ranging from about 0 to about 10 percent based on the volume of the polymeric material, and the at least one outer layer may be present in a volume ranging from about 0.01 to about 10 percent based on the volume of the polymeric material. Methods of making such polymeric materials are also described, as are apparatus for providing foamed polymeric materials.