Multiscale modeling has become an indispensable tool in condensed matter physics, physical chemistry, engineering, and materials science. One prominent class of materials, whose properties can rarely be understood on one length and time scale alone, is soft matter. Instead, by definition, the properties of soft materials are governed by structures and processes on a multitude of levels, ranging from electronic/atomic to millimeters and beyond, and from sub-picoseconds to seconds and beyond. This thesis addresses these challenges through original contributions in two areas. In the first part, we harness the capabilities of the Lattice Boltzmann Method, and couple it with coarse-grained models for both fluid-fluid and fluid-solid interfacial phenomena, to investigate the role of shape-anisotropy on colloidal self-phoresis. In particular, we provide an in-depth study of a photocatalytic, Pacman-shaped colloid with current and experimental relevance. We show that the behavior of a Pacman colloid may be rationalized based on the cooperation and competition between two phoretic mechanisms, which result in a wide range of behavior all culminating in re-alignment with the external source of motion: the illumination light. We also find that transients are accelerated by confining geometries. In the second part, we shift to atomistic resolutions, where we introduce a novel molecular dynamics tool, Constrained Path Dynamics (CPD), to sample rare events by evolving trajectories as dynamical objects with dedicated equations of motion. Exploratory calculations of the rate for a simple bistable model are presented to illustrate the theoretical merits and algorithmic challenges of the approach.

Together, these developments attempt to push the boundaries of accessible time and length scales in soft matter simulations, offering new strategies for studying complex, out-of-equilibrium systems.