In this thesis we address three computer vision problems: (1) the detection and recognition of flat text objects in images of real scenes; (2) the tracking of such text objects in a digital video; and (3) the tracking an arbitrary three-dimensional rigid object with known markings in a digital video. For each problem we developed innovative algorithms, which are at least as accurate and robust as other state-of-the-art algorithms. Specifically, for text recognition we developed (and extensively evaluated) a new HOG-based descriptor specialized for Roman script, which we call T-HOG, and showed its value as a post-filter for an existing text detector (SnooperText). We also improved the SnooperText algorithm by using the multi-scale technique to handle widely different letter sizes while limiting the sensitivity of the algorithm to various artifacts. For text tracking, we describe four basic ways of combining a text detector and a text tracker, and we developed a specific tracker based on a particle-filter which exploits the T-HOG recognizer. For rigid object tracking we developed a new accurate and robust algorithm (AffTrack) that combines the KLT feature tracker with an improved camera calibration procedure. We extensively tested our algorithms on several benchmarks well-known in the literature. We also created benchmarks (publicly available) for the evaluation of text detection and tracking and rigid object tracking algorithms.