© 2015 R. López-Esparza et al. We review briefly the concept of colloidal dispersions, their general properties, and some of their most important applications, as well as the basic molecular interactions that give rise to their properties in equilibrium. Similarly, we revisit Brownian motion and hydrodynamic interactions associated with the concept of viscosity of colloidal dispersion. It is argued that the use of modern research tools, such as computer simulations, allows one to predict accurately some macroscopically measurable properties by solving relatively simple models of molecular interactions for a large number of particles. Lastly, as a case study, we report the prediction of rheological properties of polymer brushes using state-of-the-art, coarse-grained computer simulations, which are in excellent agreement with experiments.