This book examines modern methods of creating models and measures in measurements, physical and probabilistic measures, models, spaces and bases of signals and fields, deterministic and probabilistic models and measures of angular quantities. Examples of their use on a circle and in phase measurements are given; models and measures for diagnostics in the electric power industry, in standardless measurements of the characteristics of composite materials, in environmental pollution monitoring systems, also with using unmanned aerial vehicles, are considered. Most of the presented results were obtained on the basis of the Institute of Engineering Thermophysics of National Academy of Sciences of Ukraine. The book is intended for researchers, engineers, as well as lecturers, graduate students and students of higher educational institutions dealing with the problems of measurements, monitoring and diagnostics of complex technical objects.