Multi-component fluids comprise a rich and interesting branch of fluid dynamics and complex patterns are often formed by the fluid components. In order to accurately capture the physics of such systems, multiscale modeling and computational methods are often required. In this thesis we focus in two areas of the computation and simulation of complex fluids: Phase separating fluids in the presence of thermal fluctuations and Coupled flow-polymer dynamics. First we present an easy to implement drift splitting numerical method for the approximation of stiff, nonlinear stochastic differential equations. The method is an adaptation of the SBDF multi-step method and allows for a semi-implicit discretization of the drift term to remove high order stability constraints associated with explicit methods. For problems with small noise, of amplitude ε, we prove that the method converges strongly with order O(Δt² + εΔt + ε²Δt^1/2) and thus exhibits second order accuracy when the time-step is chosen to be on the order of ε or larger. We document the performance of the scheme with numerical examples and also present as an application a discretization of the Stochastic Cahn-Hilliard Equation that removes the high order stability constraints for explicit methods. Next we consider the modeling and simulation of polymer-flow dynamic interactions within a field-theoretic framework. Field theoretic models have been used successfully to investigate a wide range of polymer formulations at equilibrium, though they often fail to accurately capture the non-equilibrium behavior of polymers. Here the "two-fluid" approach serves as a useful alternative, treating the motions of fluid components separately in order to incorporate asymmetries between polymer molecules. In this work we focus on the connection of these two theories, drawing upon the strengths of each in order to couple polymer microstructure with the dynamics of the flow in a systematic way. We derive a model for an inhomogeneous melt of elastic dumbbell polymers, incorporating thermodynamic forces into a two-fluid model for the flow via field theory, and develop a corresponding efficient numerical methodology for the resulting system of equations. We illustrate the methodology with several examples of phase separation in an initially quiescent flow.