In the era of widespread telecommunication systems, with the consequent crowding of the frequency spectrum, microwave filters and multiplexers play a key role in the development of most communication devices. Their design and tuning can rely on some well-established techniques, but miniaturization, wide frequency ranges and the other challenges of modern engineering relentlessly push these to their limits; the present book is meant to provide theoretical advances and insights addressing some of the common issues in this field. Filters design is here examined in a way alternative to classical approaches, in an effort to extend applicability cases and allow for a synthesis outcome closer to the real-world behavior. Diagnosis and tuning are moreover typical bottlenecks in the development of diplexers; the problem is here studied to introduce techniques aimed at obtaining models of the device under test for a quicker identification of faults and mismatched elements. Basic definitions, derivation of equations and easy-to-use algorithms are among the covered topics, alongside useful circuital transformations and computational tools for application by microwave engineers and researchers.