Aircraft equipped with an electric propulsion system are of increasing interest to the aeronautical community. Facing a growing pressure to reduce pollutant emissions, noise and fuel consumption, leading aircraft manufacturers and research institutions are turning their attention to the development of high-efficiency airplanes - also called "green aircraft". Electric propulsion is currently seen as one of the main solutions to this problem and, with the continuous improvements in power sources, electric motors and control systems, manned airplanes equipped with this type of propulsion are beginning to emerge in the general aviation market segment. The increase in demand for electric aircraft has also boosted research in the field, with many new studies being published in the last few years. Although it has become a burgeoning area in aeronautical research and development, there is still a long way until commercial electric airplanes become operational. There are many theoretical and technological gaps to be filled, especially concerning power sources. Furthermore, the performance characteristics of electric propulsion are significantly different from those of internal combustion, and there is currently a strong demand to fill the existing knowledge gaps. The focus of this thesis is to develop analytical and numerical methods to analyze and understand the performance of electric airplanes, addressing energy and electric charge consumption, and the effects of this type of propulsion on the overall performance. Novel formulations are proposed to model and characterize the electric airplane, how it interacts with this new propulsion system, and how the main performance capabilities are affected. The goal is to develop analytical and numerical tools capable of estimating performance metrics such as range, endurance, electric current and charge consumption, etc. in the main flight phases. Parametric descriptions of the relevant aircraft systems are developed, and expressions for the performance metrics are formulated, taking into account particular characteristics of the main components and power sources. The optimal conditions for the metrics are also investigated, and analytical solutions to some optimization problems are derived and presented in parametric form. In addition, numerical simulations using an example electric aircraft are carried out to validate the proposed methodology, and to provide quantitative insight into the performance problems.