Image point correspondence is a key problem in many applications of computer vision, such as object detection, object recognition, 3D reconstruction, image registration and video understanding. Due to a large family of image types, various shape distortions, and diversity of applications, the correspondence problem has been a challenging problem for a long time. In this dissertation, the main work is focused on the implementations of some state-of-art algorithms, as well as their applications. It can be summarized as: The SIFT (Scale Invariant Feature Transform) is implemented for image point correspondences. In this algorithm, firstly keypoints are detected by DoG (Difference-of-Gaussian) operator and refined in the image scale space. Then a dominant orientation is assigned and a local image descriptor is computed for each keypoint. Finally keypoints are matched using the Euclidean distance between descriptors. SIFT features are invariant to complicated image transformations and distinctive enough for matching. Experimental tests demonstrate the stability of our SIFT implementation. In some applications like 3D reconstruction, a large quantity of high accuracy corresponding points are needed. To this end, a match propagation software is implemented to get Quasi-Dense point correspondences with even distribution and sub-pixel accuracy. In this thesis, a coarse to fine matching strategy is adopted to obtain seed matches, which combines SIFT features with some global geometric constraints. In addition, a correlation method is adopted to refine the point into sub-pixel accuracy. Obtained seed matches can be used for propagation of reliable point correspondences. The software is applied to 3D reconstruction of wide-ranging scenes, and satisfactory results are obtained. A SIFT feature based matching method is proposed for video shot detection, and two different measure schemes are introduced, namely pair-wise based matching and chain matching. Shot boundaries are detected by analyzing temporal evolution of the number of matched SIFT features across frames. In this method, all kinds of shot transitions are detected within the same scheme, with the advantages of avoiding model selection and parameter adjustment. SIFT features are applied to remote sensed image matching. Control points are computed using SIFT descriptors and refined through optimization under an affine model. Then the refined control points are used for control region registration. Besides, match propagation is applied to aerial image matching, and preliminarily encouraging results are obtained.