The processes of injection molding (RM), blow molding(BM), thermoforming(TF) and rotational molding(RM) have been used for many years for the production of hollow parts. Recently, several types of additive manufacturing have been developed. Mathematical modeling has had an enormous impact on IM, some impact on BM, TF and RM.Currently, significant efforts are devoted for understanding the additive manufacturing processes of selective laser sintering (SLS) and fused deposition modeling (FDM). Injection molding is very fast while rotational molding and additive manufacturing are very slow. The mechanical properties of the parts are influenced by several parameters. Bond strength seems to be the most important parameter for the determination of the properties of parts produced by SLS and FDM. Tooling cost, cycle time, market size and cost per part are usually the most important considerations in deciding which process to use. During the presentation, the challenges in mathematical modeling of IM, BM, TF, RM, SLS and FDM will be reviewed. Also, various aspects relating to raw material, tooling and part characteristics will be discussed.