As both buildings and power systems undergo rapid decarbonization, demand flexibility (DF) in buildings has emerged as a key enabler for renewable energy integration, grid reliability, energy resilience, and efficient and low carbon operation. By dynamically adjusting building energy use in response to grid requirements, DF can help reduce building operational costs, respond to renewable variability, reduce peak demand, alleviate network congestion, and enhance overall system stability. Consequently, significant research efforts have examined building DF from multiple perspectives, including flexibility definitions, resources, characterization, assessment, optimization, and application scenarios. However, the effective delivery of DF in buildings requires an integrated, end-to-end approach spanning perception, cognition, decision, execution, and verification, which remains a critical gap in the existing literature. This review addresses this gap by proposing a layered architecture that integrates these stages into a coherent framework and provides insights from existing studies in this field. It synthesizes enabling methods, clarifies cross-layer interactions, and examines how data, models, control strategies, implementation mechanisms, and evaluation approaches collectively support DF delivery. Critical cross-layer challenges are identified, and future research priorities for robust and trustworthy DF delivery are outlined. This work establishes a conceptual foundation for advancing interoperable, grid-responsive, and practically deployable DF solutions in buildings, supporting both building decarbonization and more efficient, resilient grid operation