This monograph describes mathematical techniques for various aspects of flexural gravity wave propagation, pertinent to ocean engineering. It focuses on frontier problems in hydroelasticity including blocking dynamics of flexural gravity waves in both homogeneous and stratified fluids. Various wave-structure interaction problems with similar dispersion relations are revisited and solutions are demonstrated through real-life physical problems. It covers developments in the frequency and time domain analysis of wave-structure interactions. Provides comprehensive theoretical analysis and mathematical techniques crucial for advancing research in hydroelasticity, wave-structure interactions, and related fields Offers practical design solutions and methodologies applicable for development of VLFSs, offshore platforms, and coastal structures Focusses on both frequency- and time-domain problems, and both linear and nonlinear problems Methods used for wave scattering by harmonic propagating waves are generalized to deal with multiple propagating waves in the context of blocking dynamics. Various problems are discussed in two dimensions and in three dimensions in the case of oblique waves This book is aimed at graduate students and researchers in marine hydrodynamics, ocean engineering, wave-structure interaction and applied mathematics.