The Rice Convection Model (RCM) is a numerical model that self-consistently computes electric fields and plasma flows and utilises a multi-fluid approach to calculate adiabatic particle drift motions in coupled planetary magnetospheres and ionospheres. For forty years the RCM has provided insights into the complex physical magnetospheric dynamics and interactions occurring both terrestrially and at the outer planets. The underlying assumptions made in order to obtain the equations solved to construct the RCM are examined, the individual physical contributions permitted identified and the impacts of contributions prohibited considered. The mathematical equations, numerical techniques and computational logic combined to construct the model can then be clearly presented and described. Consideration is then given to the set-up of the computational domain inside which these operations are carried out to form the RCM. Completing this in-depth review of the RCM allows for a deep analysis of the results computed by the model. This provides an understanding of the physical phenomenon that are captured and explained by the model and those that are beyond the limitations of it currently. Special emphasis will be placed on plasma flows which exhibit the Radial-Interchange instability.