This book analyzes the unsteady, viscous flow-field of an oscillating airfoil. This has ramifications on understanding the flapping flight of natural biological systems like fishes and invertebrates. It also helps towards a better aerodynamic design and understanding of flapping types MAVs. The flow-field simulation is performed with a grid-free Lagrangian particle based solver using vorticity particles. An examination of the unsteady aerodynamic load and the qualitative wake structures are done for airfoils undergoing pitch and plunge oscillations. The propulsive behavior is investigated at medium to high frequency ranges for different relevant parameters. These are amplitude of oscillation, mean angle of attack, and rotational axis location. Asymmetric sinusoidal motions are also examined. Dynamic stall is another important aspect of unsteady aerodynamics that airfoils and wings experience during their time dependent movement at large angles of attack. Insects use this phenomenon to increase the aerodynamic loads during their large angle flapping maneuvers. This aspect is also studied in this book.