The aim of this thesis is to take a broad conceptual overview of the global energy system and investigate what the aims of sustainability might entail for such a system. The work presented uses a biophysical economic approach in that the dynamics of the global economy are investigated using the tool box of the physical sciences, including the laws of thermodynamics and the methods of energy analysis. Modern society currently uses approximately 500 exajoules (EJ = 10^18 J) of total primary energy supply (TPES) each year. This energy consumption has been increasing at roughly 2% per year for the past two hundred years. TPES is currently dominated by three non-renewable energy sources: coal, oil and gas which, together with energy from nuclear fission of uranium, make up around 85% of the energy market. Consumption of finite resources at a continuously growing rate is not sustainable in the long-term. A trend in policy direction is to seek a transition to renewable sources of energy. This thesis seeks to explore two questions: are the technical potentials of renewable energy sources enough to supply the current and/or projected demand for energy and what would be the effect on the physical resource economy of a transition to an energy supply system run entirely on renewable energy sources? The Global Energy Model using a Biophysical Approach (GEMBA) methodology developed here is compared and contrasted with other approaches that are used to study the global energy-economy system, including the standard neoclassical economic approach used in such models as MESSAGE and MARKAL. A number of meta-analyses have been conducted in support of the GEMBA model. These include: meta-analysis of historic energy production from all energy sources; meta-analysis of global energy resources for all energy sources; meta-analysis of energy-return-on-investment (EROI) for all energy sources. The GEMBA methodology uses a systems dynamic modelling approach utilising stocks and flows, feedback loops and time delays to capture the behaviour of the global energy-economy system. The system is decomposed into elements with simple behaviour that is known through energy analysis. The interaction of these elements is captured mathematically and run numerically via the systems dynamics software package, VenSim. Calibration of the model has been achieved using historic energy production data from 1800 to 2005. The core of the GEMBA methodology constitutes the description of a dynamic EROI function over the whole production cycle of an energy resource from initial development, through maturation to decline in production, in the case of non-renewable resources, or to the technical potential in the case of renewable resources. Using the GEMBA methodology, the global energy-economy system is identified as a self-regulating system. The self-regulating behaviour acts to constrain the amount of total primary energy supply that the system can produce under a renewable-only regime. A number of analyses are conducted to test the sensitivity of the system to such changes as: an increase of the technical potential of renewable resources; technological breakthroughs which would significantly increase the EROI of renewable resources; a decrease in the capital intensity of renewable resources and; an increase in the energy intensity of the economy, A statistical analysis reflecting the wide range of values of both the estimates of EROI and technical potentials of renewable energy sources has also been undertaken using a Monte Carlo approach. The results from the modelling suggest that not all levels of energy demand projected by the WEA can be supplied by an energy system running solely on renewable energy. The Monte Carlo analyses suggest that reduction in total energy yield over current (2010) levels might occur with a 20-30% possibility. The middle and high growth scenarios from the WEA are greater than 95% of all scenarios modelled, hence seem unlikely to be sustained by an energy system running solely on renewable energy. This finding has implications for the future direction of both engineering and technology research as well as for energy policy. These implications are discussed.