The objective of this paper is to compare the existing methods and develop novel approaches for the experimental data analysis of the unsteady aerodynamics of the flapping wing microaerial-vehicle. These methods are developed for the purpose of identification of the beneficial dynamics and for the development of reduced order models for control design. We first employ Proper Orthogonal Decomposition (POD) method for the data analysis of the PIV measurements in the wakes of piezoelectric flapping wings. The basic idea behind POD based data analysis method is to decompose the time series snapshots of PIV measurements into high energy, POD, modes. The POD modes obtained from the PIV measurement data with different control inputs, such as flapping amplitude, angle of attack and flight speed, are compared to identify high energy modes that are invariant across the range of operating conditions. Similarly the modes that are responsible for maximum energy transfer between the control inputs and the desired output such as lift and thrust are identified. The second method that we propose for the PIV data analysis is inspired from our recent work to develop a novel approach for the spectral analysis of the nonlinear flows. This new method is based on the spectral analysis of the linear transfer operator, the so called Koopman operator, associated with any nonlinear flows. The motivation for this work comes from the desire to perform frequency-based decomposition of the snapshot data as opposed to energy based decomposition in the POD method. While POD-based data analysis method captures all high energy content modes, it ignores the low energy content modes. These low energy modes might play an important role from the dynamics point of view and hence cannot be ignored. We perform the spectral analysis of the linear transfer, Perron-Frobenius (P-F) operator, which is dual to the Koopman operator to obtain the frequency based decomposition of the time series snapshot data. The basic idea behind this approach is to construct the finite dimensional approximation of the linear transfer (P-F) operator that best describes the time evolution of the snapshots data. The eigenvalues and eigenvectors of this transfer operator carry useful information about the system dynamics.