The link between various viscoelastic fluids models and the symmetric matrix Riccati differential equations can be a new device that brings to unified and proper ways of numerical treatments for the viscoelastic models. In this talk, we describe a few steps toward efficient numerical schemes for complex fluids simulation. First, we construct stable finite element discretizations using Eulerian--Lagrangian methods based on the Riccati formulations of the viscoelastic models. Then we develop a new multilevel time-marching scheme; together with adaptive time-stepping schemes and time parallel schemes, we can build efficient methods for complex fluids simulation. Furthermore, we discuss two robust and efficient multilevel solvers for Stokes-type systems arising at each time step in the Eulerian--Lagrangian discretization.