Non-linear surface impedance is a significant limitation for microwave superconducting devices operating at high microwave power levels. This book describes the non-linear lossess of high temperature superconductors at high frequency. A novel model is developed to explain the non-linear surface impedance of high temperature superconductors. Different non-destructive microwave characterisation techniques are also illustrated in this book. The developed model is verified against the measured surface impedance data.