Aggregation phenomena in colloidal systems with and without shear flow studied with mesoscale Langevin Dynamics method is a primary focus of the current study. Applicability of mesoscale methods to the non-equilibrium time evolving systems (considered in the current study) is limited due to need for the potential of mean force. Available coarse-graining (CG) approaches are suitable for equilibrium system only. To resolve this issue a coarse-graining approach is developed to infer mesoscale interaction potentials in aggregating systems, resulting in an improved potential of mean force for Langevin dynamics (LD) and Brownian dynamics (BD) simulations. Starting from the evolution equation for the solute pair correlation function, this semi--analytical CG approach identifies accurate modeling of the relative acceleration between solute particles in a solvent bath as a reliable route to predicting the time--evolving structural properties of non--equilibrium aggregating systems. Noting that the solute--solvent pair correlation function attains a steady state rapidly compared to characteristic aggregation time scales, this CG approach derives the effective relative acceleration between a pair solute particles in the presence of this steady solute--solvent pair correlation by formally integrating the solvent force on each solute particle. This results in an improved potential of mean force that explicitly depends on the solute--solute and solute--solvent pair potentials with the capability of representing both solvophilic and solvophobic interactions that give rise to solvation forces. This approach overcomes the difficulty in specifying the LD/BD potential of mean force in aggregating systems where the solute pair correlation function evolves in time, and the Kirkwood formula U(r) = - k T ln g(r) that is applicable in equilibrium diffusion problems cannot be used. LD simulations are compared with molecular dynamics (MD) simulations for a model colloidal system interacting with Lennard-Jones pair potentials to develop and validate the improved potential of mean force. LD simulations using the improved potential of mean force predict a solute pair correlation function that is in excellent match with MD in all aggregation regimes, whereas using the unmodified MD solute-solute pair potential in LD results in a poor match in the reaction--limited aggregation regime. The improved potential also dramatically improves the predicted extent of aggregation and evolution of cluster size distributions that exhibit the same self--similar scaling found in MD. This technique of coarse--graining MD potentials to obtain an improved potential of mean force can be applied in a general multiscale framework for non--equilibrium systems where the evolution of aggregate structure is important. For a complete description of aggregating phenomena numerical simulation of non-sheared and sheared colloidal particles aggregation in model systems is performed by using Langevin dynamics model with improved interparticle interaction potential. For these systems the set of dimensionless parameters that is able to distinguish scale--separated and scale--overlap regimes was determined. The aggregates restructuring process due to shear flow is captured by the energy evolution analysis as such that allows to capture redistribution of the flow energy into the fluctuating energy which is the source of the aggregates restructuring. With this energy analysis a fundamental understanding of restructure and/or breakage processes that caused by imposed shear flow is gained. The effect of shear flow onto the local and global structure of aggregates is studied with the local volumetric potential energy density LPED and the maximum radius of gyration Rg correspondently. It is observed that shear flow dramatically change the structure of aggregates on both local and global length scales. On the local length scale shear flow cases the formation of more or less compact structures depending on the shear flow intensity characterized by P`eclet number Pe. On the global length scale the size of aggregates in the direction perpendicular to the shear flow is limited by Rg and its value depends on the Pe as well. A new method for Rg prediction that yields results consistent with those obtained from the direct size distribution calculations is proposed. With full analysis of the sheared aggregating systems the aggregating map based on new metric $f_{pot,sh}$ which is the ratio of interparticle force to the

shear force is proposed. This map allows to determine different aggregating outcomes based on the initial parameters of the sheared aggregating systems such as interparticle force and shear flow rate. This map can be used when planning new aggregating experiments or when comparing outcomes from several different aggregating systems.