We present a method for space-time completion of large space-time "holes" in video sequences of complex dynamic scenes. The missing portions are filled-in by sampling spatio-temporal patches from the available parts of the video, while enforcing global spatio-temporal consistency between all patches in and around the hole. This is obtained by posing the task of video completion and synthesis as a global optimization problem with a well-defined objective function. The consistent completion of static scene parts simultaneously with dynamic behaviors leads to realistic looking video sequences. Space-time video completion is useful for a variety of tasks, including, but not limited to: (i) Sophisticated video removal (of undesired static or dynamic objects) by completing the appropriate static or dynamic background information, (ii) Correction of missing/corrupted video frames in old movies, and (iii) Synthesis of new video frames to add a visual story, modify it, or generate a new one. Some examples of these are shown in the paper.