The book "Models and Phenomena in Fracture Mechanics" offers a comprehensive introduction to modern concepts in fracture mechanics. It addresses both homogeneous and structured models, highlighting the role of microstructure in fracture and phase transitions. The content begins with a detailed examination of one-dimensional models that allow for the understanding of essential phenomena without technical difficulties. Subsequently, more realistic models are considered, including linear and nonlinear elastic media, elastic plates with crack closure, as well as viscoelastic discrete lattices and cohesive zone models. The book also covers topics such as crack initiation, equilibrium, and the slow and fast growth of cracks. Additionally, various crack speed regimes and their transitions are analyzed. The application of the Fourier transform and related topics, including a version of the Wiener-Hopf technique, are also discussed. This specialized book is aimed at researchers, educators, and advanced students in the field of materials and structural sciences.