In this talk we shall discuss the monolithic Newton multigrid FEM approach for the simulation of general nonlinear incompressible flow problems with complex rheology. The governing equations arise from model problems with nonisothermal behavior, pressure and shear dependent viscosity in viscoelastic fluids. The well-known HWNP is overcome with LCR formulation wich guarantees the positive definiteness of the discrete conformation tensor. The coupling between the velocity gradient and the elastic stress, which leads to the restriction for the choice of FEM approximation spaces, and the hyperbolic nature of the problem are handled with edge-oriented stabilization. The nonlinearity is treated with Newton-type solver for nonregular problems taking into account the special properties of the partial operators which arise due to the differentiation of the corresponding nonlinear viscosity function. The resulting linearized system inside of the outer Newton solver is a typical nonsymmetric saddle point problem is solved using the geometrical multigrid with a Vanka-like smoother. Based on the existing software packages for the numerical simulation of complex fluid flows (FeatFlow), the new numerical methods and algorithmic tools have been used to deal with the challenging models, as for instance, granular material, particulate flow, or viscoelastic fluid models. We present some realistic examples of nonlinear fluids which are modeled by non-Newtonian models in complex geometry to illustrate some of these numerical techniques Key words: Monolitic, Viscoelastic flow, LCR reformulation, Edge-Oriented stabilization, Finite Element Method, Newton method, multigrid solver, Vanka smoother