The issue of fundamental limitations in filtering and control lies at the very heart of any feedback system design, since it reveals what is and is not achievable on the basis of that system's structural and dynamic characteristics. Alongside new succinct treatments of Bode's original results from the 1940s, this book presents a comprehensive analysis of modern results, featuring contemporary developments in multivariable systems, sampled-data, periodic and nonlinear problems. The text gives particular prominence to sensitivity functions which measure the fundamental qualities of the system, including performance and robustness. With extensive appendices covering the necessary background on complex variable theory, this book is an ideal self-contained resource for researchers and practitioners in this field.