An outline is given of the physical basis and of the derivation of the Langevin and Fokker-Planck equations which are the fundamental equations used to describe the dynamics of colloidal particles in a suspension. The calculation of the hydrodynamic interaction tensors which describe the effect of the background fluid flow on the motion of the suspended particles is identified as a major problem in the application of this fundamental theory. Thus, the evaluation of these tensors is extensively discussed. An outline is also presented of the calculation of the bulk properties of a suspension, in particular, the scattering functions and the various diffusion constants required to characterising a suspension. This is because the Langevin or Fokker-Planck equations only provide a partial description of the dynamics of the system and, thus, special formulae must be derived for the calculation of bulk properties of suspensions from this limited data. Since the basic equations are very difficult to solve analytically a description is given of the numerical Brownian Dynamics (BD) method used for the computer simulation of the static and dynamic properties of suspensions based on the Langevin or Fokker-Planck equation. Also presented is a discussion of what has been learnt from the application of the BD method to particular systems and what limitations the method possesses. Finally, we speculate on possible applications of the BD method.