In nature there are many systems that exhibit some form of self-organization. Among these are forest fires, earthquakes, sandpiles, maybe sunspots and even life itself. Investigations into the similarity of the dynamics of such systems have been undertaken by using simple cellular automata models. These models have produced some important insight into the dynamics of such systems. Recently a Self-Organized Criticality (SOC) model for turbulent transport in magnetically confined plasmas has been proposed in order to explain some of the observed features of the transport dynamics in these plasmas. This model is based on the dynamics of a sandpile and has among others, the remarkable feature that a sheared wind across the sandpile (or a flow across the plasma) can fundamentally change the transport. The dynamics of the model show some remarkably similar characteristics to the observed data and suggest explanations for some puzzling aspects of the observations. Adding new, physically realistic, dynamical transport mechanisms such as classical diffusion to the SOC system have been found to lead to a new set of dynamical regimes with evidence of critical transitions between them. These regimes can then be explored in the plasma experiments. In addition to the intrinsic novelty of the basic physics involved, these observations can have interesting ramifications for the control of many real systems. Some of these features of the SOC systems, from forest fires to earthquakes, and the extension to the sandpile model for turbulent transport will be discussed as well as their connection to fusion plasmas.