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The design of resilient and sustainable buildings (RSB) is a challenging task owing in part to the consideration of various economic, sustainability, resilience, and other metrics while making decisions about a system comprised of subsystems, each generally consisting of numerous components. The combination of metrics and subsystems translates into numerous feasible design alternatives from which one must be selected. This chapter aims to provide an overview of the mathematical basis for the development of the sequential decision process (SDP), its various extensions and relevant applications, and examples to illustrate its use for the design of RSB. It begins with a review of the concept of viewing design as an SDP to provide the necessary background information. Key concepts pertaining to the development of low-fidelity models to bound the precise values of decision criteria, sequencing the low-fidelity models for efficient tradespace exploration, and calculating optimal modeling policies are described.