Rheological equations of state are of great importance for simulation of polymer processing and for characterization of polymer melts. We consider tube model based constitutive equations developed in the last 40 years since the original publication of Doi and Edwards in 1978. The emphasis is on the concepts, assumptions, and material parameters introduced to model nonlinear viscoelasticity of polydisperse linear and long-chain branched (LCB) polymer melts, and the scope is limited to constitutive equations which can be expressed in terms of integral, differential, or integro-differential equations. Multi-mode models based on the concept of pre-averaged stretch such as the rolie-poly and the pom-pom models require a large number of nonlinear model parameters. Relaxing the assumption of a constant tube diameter, the number of nonlinear model parameters can be drastically reduced to 2 or 3, independent of the number of Maxwell modes needed to represent the linear viscoelasticity. The most recent constitutive model for linear and LCB polymer melts, the HMMSF model, requires only one parameter (the dilution modulus GD) for modeling extensional flows, and one additional parameter for accounting constraint release in shear flows, independent of the number of Maxwell modes used to define linear viscoelasticity.