Injection molding systems and methods useful for making microcellular foamed materials are provided as well as microcellular articles. Pressure drop rate and shear rate are important features in some embodiments, and the invention provides systems for controlling these parameters in an injection molding system. Another aspect involves an injection molding system including a nucleator that is upstream of a pressurized mold. Another aspect involves an extrusion system with the reciprocating screw for forming a single phase solution of non-nucleated blowing agent and polymeric material. Another aspect involves very thin walled microcellular material and very thin walled polymeric material. Another aspect provides a method for producing high weight reductions in very thin-walled parts with surfaces that have no noticeable differences from non-foamed parts.