Object classes are central to computer vision and have been the focus of substantial research in the last fifteen years. This thesis addresses the tasks of localizing entire objects in images (object class detection) and localizing their semantic parts (part detection). We present four contributions, two for each task. The first two improve existing object class detection techniques by using context and calibration. The other two contributions explore semantic part detection in weakly-supervised settings. First, the thesis presents a technique for predicting properties of objects in an image based on its global appearance only. We demonstrate the method by predicting three properties: aspect of appearance, location in the image and class membership. Overall, the technique makes multi-component object detectors faster and improves their performance. The second contribution is a method for calibrating the popular Ensemble of Exemplar- SVM object detector. Unlike the standard approach, which calibrates each Exemplar- SVM independently, our technique optimizes their joint performance as an ensemble. We devise an efficient optimization algorithm to find the global optimal solution of the calibration problem. This leads to better object detection performance compared to using independent calibration. The third innovation is a technique to train part-based model of object classes using data sourced from the web. We learn rich models incrementally. Our models encompass the appearance of parts and their spatial arrangement on the object, specific to each viewpoint. Importantly, it does not require any part location annotation, which is one of the main limits to training many part detectors. Finally, the last contribution is a study on whether semantic object parts emerge in Convolutional Neural Networks trained for higher-level tasks, such as image classification. While previous efforts studied this matter by visual inspection only, we perform an extensive quantitative analysis based on ground-truth part location annotations. This provides a more conclusive answer to the question.