In many countries, any new building design must undergo formal regulatory assessment before construction can commence. This process has historically involved a combination of manual methods, logical reasoning, mathematical analysis, and expert judgment. Over recent decades, however, the volume of building regulations has expanded substantially, slowing approval processes and generating significant negative social and economic consequences, including reduced national productivity, rising construction costs, and constrained access to housing. While regulation remains essential for safety, health, and environmental performance, manual assessment processes are increasingly unable to keep pace with the growing body of rules. This situation has prompted global interest in automated compliance checking (ACC) systems that use mathematical and computational logic to evaluate regulatory requirements. Where regulations are explicitly and quantitatively defined, ACC has proven effective. However, regulations framed in qualitative, contextual, or discretionary terms resist straightforward mathematical formalization and remain largely beyond current automation. This chapter explains the types of building codes that exist and their varying mathematical structures and framing. It then presents an overview of established and emerging ACC approaches that address these technical, social, and environmental challenges. The chapter uses illustrative examples of codes and rules, similar to those found across multiple countries, to describe the scope and format of building regulations and the mathematical approaches used to assess them.