This volume contains a series of articles on wave phenomena and fluid dynamics, highlighting recent advances in these two areas of mathematics. The collection is based on lectures presented at the conference Fluids and Waves--Recent Trends in Applied Analysis and features a rich spectrum of mathematical techniques in analysis and applications to engineering, neuroscience, physics, and biology. The mathematical topics discussed range from partial differential equations, dynamical systems and stochastic processes, to areas of classical analysis. This volume is intended as an introduction to major topics of interest and state-of-the-art analytical research in wave motion and fluid flows.