Experimental evidence are collected together to show in general the viscoelastic mechanisms of low and high molecular weight polymers have different dependences on temperature T, pressure P, and the same scaling product variable, TV gamma, where V is the specific volume and gamma is a material constant. The viscoelastic mechanisms include the JohariGoldstein beta-relaxation, the segmental alpha-relaxation, the sub-Rouse modes, the Rouse modes, and the terminal relaxation if the polymer chains are entangled. Appropriately called the thermo-, piezo-, and TV'-rheological complexity of polymers, these viscoelastic anomalies are fundamental and deserve attention from the polymer physics community. Although we show that the coupling model can rationalize the origin of the complexity and explain some of the data quantitatively, the objective of this paper is to stimulate others to construct a theory that can do even better.