A variety of methods of forming polymer manifolds and the resulting manifold structures are described. The described manifolds are well suited for use in heat exchangers and a variety of other applications. In one aspect a polymer manifold includes a multiplicity of tubes having first ends that are received by a manifold housing. A polymer film is secured to the manifold housing and to the ends of each of the tubes. The film is arranged to seal the housing while leaving the openings of the tubes exposed to thereby create a manifold. In some embodiments, a potting material is used to reinforce the film. In a method aspect, a manifold may be formed by positioning first ends of the tubes in a manifold housing and welding a polymer film to the manifold housing and to distal tips of the tubes. Openings for the tubes are then formed in the film by directing heat towards the film which melts or vaporizes the film in the regions of the tube openings. A liquid coolant or potting material is placed inside of the chamber within the manifold housing that is sealed by the film during the heating to help prevent the heat from damaging the seals between the film and the tube tips or the film in the interstitial spaces between the tubes.