With the advent of exascale architectures maximizing performance while maintaining energy consumption within reasonable limits has become one of the most critical design constraints. This constraint is particularly significant in light of the power budget of 20 MWatts set by the U.S. Department of Energy for exascale supercomputing facilities. Therefore, understanding an application's characteristics, execution pattern, energy footprint, and the interactions of such aspects is critical to improving the application's performance as well as its utilization of the underlying resources. With conventional methods of analyzing performance and energy consumption trends scientists are forced to limit themselves to a manageable number of design parameters. While these modeling techniques have catered to the needs of current high-performance computing systems, the complexity and scale of exascale systems demands that large-scale design-space-exploration techniques are developed to enable comprehensive analysis and evaluations. In this dissertation we present research on performance and energy modeling of current high performance computing and future exascale systems. Our thesis is focused on the design space exploration of current and future architectures, in terms of their reconfigurability, application's sensitivity to hardware characteristics (e.g., system clock, memory bandwidth), application's execution patterns, application's communication behavior, and utilization of resources. Our research is aimed at understanding the methods by which we may maximize performance of exascale systems, minimize energy consumption, and understand the trade offs between the two. We use analytical, statistical, and machine-learning approaches to develop accurate, portable and scalable performance and energy models. We develop application and machine abstractions using Aspen (a domain specific language) to implement and evaluate our modeling techniques. As part of our research we develop and evaluate system-level performance and energy-consumption models that form part of an automated modeling framework, which analyzes application signatures to evaluate sensitivity of reconfigurable hardware components for candidate exascale proxy applications. We also develop statistical and machine-learning based models of the application's execution patterns on heterogeneous platforms. We also propose a communication and computation modeling and mapping framework for exascale proxy architectures and evaluate the framework for an exascale proxy application. These models serve as external and internal extensions to Aspen, which enable proxy exascale architecture implementations and thus facilitate design space exploration of exascale systems. / Ph. D.