Widespread application of digital video images has increased the demand to store such data in finite memory space and to transmit them over channels with limited bandwidth. This increasing demand represents a critical need to compress video images. Current video compression methods, which use motion estimation to remove temporal redundancy in consecutive video frames, divide images into blocks or meshes. Block-based methods are not capable of distinguishing movements that involve rotation, shear, zoom-in or zoom-out. Moreover, these methods assume the same motion for all pixelin a block. The required time for motion estimation is an important bottleneck in full search algorithms. Mesh-based methods can model different kinds of motions by mathematical functio however, they are computationally more expensive than block-based techniques. In this thesis, several block and mesh based methods are reviewed. Then, a method for fast motion estimation and another method, which increases the peak signal-to-noise ratio (R), are proposed. The first method adaptively adjusts the size of the search window in each frame; consequently, for frames with limited motions, only a small number of operations are used. Hence, run-time will decrease significantly without compromising image quality. In the second proposed method, motion estimation is performed using hybrid block and mesh based methods. This is done by reconstructing each block with the method that minimizes reconstruction error. As a result, significant improvements ithe quality of reconstructed images are achieved, using R criterion.