In the tasks of image representation, recognition and retrieval, a 2D image is usually transformed into a 1D long vector and modelled as a point in a high-dimensional vector space. This vector-space model brings up much convenience and many advantages. However, it also leads to some problems such as the Curse of Dimensionality dilemma and Small Sample Size problem, and thus produces us a series of challenges, for example, how to deal with the problem of numerical instability in image recognition, how to improve the accuracy and meantime to lower down the computational complexity and storage requirement in image retrieval, and how to enhance the image quality and meanwhile to reduce the transmission time in image transmission, etc. In this paper, these problems are solved, to some extent, by the proposed Generalized 2D Principal Component Analysis (G2DPCA). G2DPCA overcomes the limitations of the recently proposed 2DPCA (Yang et al., 2004) from the following aspects: (1) the essence of 2DPCA is clarified and the theoretical proof why 2DPCA is better than Principal Component Analysis (PCA) is given; (2) 2DPCA often needs much more coefficients than PCA in representing an image. In this work, a Bilateral-projection-based 2DPCA (B2DPCA) is proposed to remedy this drawback; (3) a Kernel-based 2DPCA (K2DPCA) scheme is developed and the relationship between K2DPCA and KPCA (Scholkopf et al., 1998) is explored. Experimental results in face image representation and recognition show the excellent performance of G2DPCA.