Process Hazard Analysis (PHA) and Hazard and Operability Studies (HAZOP) are foundational elements of process safety management. However, complex hazards involving rare high consequence events, intricate process or instrumentation interactions, human factors, and other uncertainties require a more comprehensive and quantitative approach for proper risk assessment and management. This presentation explores limitations of PHA and HAZOP and identifies categories of complex hazards that are better suited for Quantitative Risk Assessment (QRA) and Fault Tree Analysis (FTA). The case studies presented show that an integrated approach provides a defensible, data-driven basis for risk-based decision-making.