The art, science, and engineering of thermoforming or biaxially stretching heated polymeric sheet has evolved substantially since three monographs on the subject were published in 1987. This review article updates the author's monograph [27] in the following rapidly developing areas: (a) newer thoughts on the constitutive equations of state for rubbery viscoelastic sheet; (b) the arithmetic of plane strain stretching during plug-assist thermoforming; (c) current schools of thought regarding finite element analysis, geometric analysis, and hybrid analysis for determining material distribution in thermoformed parts; (d) the unique constraints on crystallizing polyethylene terephthalate (CPET) for dual ovenable food container applications; (e) new criteria for thermoforming of multilayer rigid sheet; (f) protocols for determining steady-state physical property values in processing where regrind exhibits some property loss; and (g) some newer thoughts on the differences and similarities between pressure forming and conventional vacuum forming. It is hoped that this material bridges the gap between the current crop of monographs and those manuscripts that are currently being written.