Since the occurrence of earthquakes and their properties are very uncertain even with the present knowledge, it is too difficult to define reasonable design ground motions especially for important buildings. In the seismic resistant design of building structures, the concept of 'performance-based design' has become a new paradigm guaranteeing the maximum satisfaction of building owners. The quality and reliability of the performance-based design certainly depend on the scientific rationality of design ground motions. In order to overcome this problem, a new paradigm has to be posed. To the author's knowledge, the concept of 'critical excitation' and the structural design based upon this concept can become one of such new paradigms. This book introduces a new probabilistic and energy-based critical excitation approach to overcome several problems in the scientific and rational modelling of ground motions. The author hopes that this book will help the development of new seismic-resistant design methods of buildings for such unpredicted or unpredictable ground motions. This is the first comprehensive book for critical excitation methods. It includes updated, cutting-edge research. It is applicable to other worst-case analysis problems. It includes comprehensive review of critical excitation methods. It also includes verification by comprehensive recorded ground motions.