The computation of the interaction between turbulence and finite-sized inertial particles occurs in a wide range of scales and has proven to put heavy demands on computational models. In this talk, I will discuss higher-order Eulerian-Lagrangian models and algorithms that we have recently developed with the aim of improving accuracy and computational efficiency of particle-laden flow computation. I will discuss Eulerian-Lagrangian methods that are based on a combination of particle methods and higher-order methods such as Discontinuous Galerkin methods and WENO methods. Particular attention will be given to the higher-order projection of singular particle methods onto higher-order bases and regularization of interpolation near discontinuities.