This dissertation, divided into three parts and funded by the multinational company Synthomer LTD, is devoted to the modelling of the complex dynamics among colloidal particles in soft matter systems which are influenced by the interplay between Brownian motion, the common denominator among all the projects, and other phenomena such as inter-particle interactions and external fields. Since the Brownian motion and its interplay with shear flow and physico-chemical interactions has a clear impact on the spatial arrangement, also called microstructure, of a colloidal suspension the first part of the thesis focuses on the proposal of a new theoretical framework which analyses the aforementioned feature of diverse dispersions under strongly sheared conditions by analytically solving the 2-Body Smoluchowski equation. The obtained solution is an extension of already existing theories and it is able to recover previous results for hard-spheres fluids under semi-dilute conditions. The new framework has also unveiled a new rich physical behavior by studying the microstructure of two paradigmatic cases of physically relevant interactions, the attractive Lennard-Jones potential and the Debye-Hückel or Yukawa potential for charge-stabilized particles. The Brownian motion is also crucial in determining the aggregation behavior of colloidal particles: the mechanism proposed by Smoluchowski to study the collision rate between Brownian particles and a stationary one is used nowadays to describe the entry and exit of radicals during an emulsion polymerization. The second part of the thesis is then dedicated to the development of a mathematical model which, by using the pseudo-homopolymerization approach, describes the kinetics of this polymerization mode. By using the state-of-the-art models for radical entry and desorption the framework has the ultimate goal of predicting crucial kinetic variables such as the monomers conversions and latex composition throughout the process. The model foresees a series of unknown parameters which have been determined by extensive calibration on three different test cases of increasing complexity: a homo-polymerization of n-BA, a co-polymerization involving n-BA and methyl methacrylate (MMA) and, finally, a ter-polymerization of n-BA with MMA and 2-HydroxyEthyl Methacrylate (2-HEMA); the data for the first two series have been found in the literature, while the data for the ter-polymerization have been provided by Synthomer LTD. The predictive model has been applied to study between the surfactant surface coverage of the particles as well as the total concentration of counterions in the system in order to rationalize the coagulation behavior during the whole polymerization process. The third and final part focuses on a biological system: the self assembly of proteins in vivo. The work is focused on the growth dynamics of a poly-glutamine agglomerate, named aggresome, in a mammalian cell: through a numerical solution of the advection diffusion equation, the macroscopic equivalent of the Smoluchowski equation, it has been possible to disentangle the relative importance of Brownian diffusion and active directed cellular transport in the growth of the amyloid aggresome inside cells, thus unveiling the dominant role of diffusion over active transport.