This is the first part of a series of articles prepared for a comprehensive, international, and professional society–approved consensus project to advise on thoracic anesthesia. It represents the views and structured opinions of experts delegated to the General Management: Monitoring Task Force of the Thoracic Subcommittee of the European Association of Cardiothoracic Anaesthesiology and Intensive Care (EACTAIC). This review highlights international leaders’ main concepts and expert opinions on how monitoring is the core task of anesthesiologists involved in the care of thoracic patients, providing recommendations for assessing principal organ systems and using different devices in routine and specialized scenarios. The consensus statement addresses the following main clinical topics and questions: (1) What constitutes standard basic and advanced monitoring? (2) What are the overall goals and means of monitoring the respiratory system? (3) How shall we monitor the circulation in thoracic anesthesia? (4) What are the main aspects of monitoring neuromuscular blockade? (5) What are the best practices for monitoring the depth of anesthesia and neurologic function? (6) What are the research priorities for thoracic anesthesia monitoring? (7) The authors briefly discuss how these recommendations relate to the concepts of good clinical practice and enhanced recovery. This document was developed and formally evaluated by senior clinicians representing the core membership of the EACTAIC Thoracic Subspecialty Committee from Europe, the United States, Africa, and the Middle East. Although a high-level evidence base is generally limited and significant controversies remain, all recommendations of the Task Force achieved an agreed (>60%), strong (>80%), or sometimes full (>95%) consensus. This consensus should serve as a consolidation of diverse practices of thoracic anesthesia and a starting point toward obtaining more robust evidence to further enhance our clinical practice in the future.