Results of two doctoral theses, one using a model-based approach and the other using model-free methods, are summarized. Both included case studies of full-scale bridges. While model-based approaches are appropriate for individual infrastructure-management cases where the cost of modeling can be justified, model-free methods provide inexpensive anomaly detection for long-term monitoring of many structures. Both are compatible with civil-engineering contexts of modeling simplifications, incomplete knowledge, noise, outliers and missing data. They provide useful additions to an engineer's data-interpretation toolbox. © 2013 American Society of Civil Engineers.