The structure and dynamics of the flow field created by a plunging flat plate airfoil are investigated at a chord Reynolds number of 10,000 while varying plunge amplitude and Strouhal number. Digital particle image velocimetry measurements are used to characterize the shedding patterns and the interactions between the leading and trailing edge vortex structures (LEV and TEV), resulting in the development of a wake classification system based on the nature and timing of interactions between the leading- and trailing-edge vortices. The convection speed of the LEV and its resulting interaction with the TEV is primarily dependent on reduced frequency; however, at Strouhal numbers above approximately 0.4, a significant influence of Strouhal number (or plunge amplitude) is observed in which LEV convection is retarded, and the contribution of the LEV to the wake is diminished. It is shown that this effect is caused by an enhanced interaction between the LEV and the airfoil surface, due to a significant increase in the strength of the vortices in this Strouhal number range, for all plunge amplitudes investigated. Comparison with low-Reynolds-number studies of plunging airfoil aerodynamics reveals a high degree of consistency and suggests applicability of the classification system beyond the range examined in the present work. Some important differences are also observed. The three-dimensional flow field was characterized for a plunging two-dimensional flat-plate airfoil using three-dimensional reconstructions of planar PIV data. Whereas the phase-averaged description of the flow field shows the secondary vortex penetrating the leading-edge shear layer to terminate LEV formation on the airfoil, time-resolved, instantaneous PIV measurements show a continuous and growing entrainment of secondary vorticity into the shear layer and LEV. A planar control volume analysis on the airfoil indicated that the generation of secondary vorticity produced approximately one half the circulation, in magnitude, as the leading-edge shear layer flux. A small but non-negligible vorticity source was also attributed to spanwise flow toward the end of the downstroke. Preliminary measurements of the structure and dynamics of the leading-edge vortex (LEV) are also investigated for plunging finite-aspect-ratio wings at a chord Reynolds number of 10,000 while varying aspect ratio and root boundary condition. Stereoscopic particle image velocimetry (SPIV) measurements are used to characterize LEV dynamics and interactions with the plate in multiple chordwise planes. The relationship between the vorticity field and the spanwise flow field over the wing, and the influence of root boundary conditions on these quantities has been investigated. The viscous symmetry plane is found to influence this flow field, in comparison to other studies \cite{YiRo:2010,Vi:2011b,CaWaGuVi:2012}, by influencing tilting of the LEV near the symmetry wall, and introducing a corewise root-to-tip flow near the symmetry plane. Modifications in the root boundary conditions are found to significantly affect this. LEV circulations for the different aspect ratio plates are also compared. At the bottom of the downstroke, the maximum circulation is found at the middle of the semi-span in each case. The circulation of the $sAR=2$ wing is found to significantly exceed that of the $sAR=1$ wing and, surprisingly, the maximum circulation value is found to be independent of root boundary conditions for the $sAR=2$ case and also closely matched that of the quasi-2D case. Furthermore, the 3-D flow field of a finite wing of $sAR=2$ was characterized using three-dimensional reconstructions of planar PIV data after minimizing the gap between the plunging plate and the top stationary wall. The LEV on the finite wing rapidly evolved into an arch structure centered at approximately the 50\% spanwise position, similar to previous observations by Calderon et al. \cite{CaWaGu:2010}, and Yilmaz and Rockwell \cite{YiRo:2010}. At that location, the circulation contribution due to spanwise flow was approximately half that of the shear layer flux because of the significantly greater three-dimensionality in the flow. Increased tilting at the 25\% and 75\% spanwise locations suggests increasing three-dimensionality at those locations compared to the symmetry plane of the arch (50\% spanwise location). The deviation between the LEV circulation and integrated convective vorticity fluxes at the 50\% spanwise location suggests that entrainment of secondary vorticity plays a similar role in regulating LEV circulation as in the 2D case. While the wing surface flux of vorticity could not be measured in that case, the significant difference between LEV circulation and the known integrated fluxes is comparable to that for the 2D plate, suggesting that a significant boundary flux of secondary vorticity may exist.