Abstract: In the late 1960's the different-type simplifiedNavier-Stokes models, or as are generally called, the diffusionparabolized N-S (DPNS) equations,and their computational methods developed from the Prandtl's boundary-layertheory have correctly included the viscous-inviscid flow interacting mechanismand opened a new approach for simulating large-scale complex flowfields. Thispaper reviews the related main results of this field, includingadvantages and drawbacks of different simplified Navier-Stokes models;mathematical characteristics and their marching regularization procedures of theDPNS equations; various representative numerical solutions and theapplicability of the DPNS equations and finally the new generalized DPNSequations.