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The key to high performance of video compression lies in an efficient reduction of the temporal redundancy. For this purpose, the block-based motion estimation (BBME) technique has been successfully applied in the video compression standards from H.261 to H.264. The most straightforward BBME method must be full search algorithm (FSA) that searches every candidate position within the search range. Since FS consumes extremely high computational cost, development and refinement on ME algorithms have been fueled to archive better tradeoff between the computational cost and the ME speed. In this paper, we study the low complexity ME algorithms and classify them into three categories, namely modeling the matching error surface, fast full search and reduction of searching candidate points. In the following sections, we will have a brief review across all these categories. The aim of this review is to provide the succeeding researchers with some constructive information in design of the fast ME algorithms.