Object detection plays a critical role in various computer vision applications, encompassing domains like autonomous vehicles, object tracking, and scene understanding. These applica- tions rely on detectors that generate bounding boxes around known object categories, and the outputs of these detectors are subsequently utilized by downstream systems. In practice, supervised training is the predominant approach for training object detectors, wherein labeled data is used to train the models. However, the effectiveness of these detectors in real-world scenarios hinges on the extent to which the training data distribution can adequately represent all potential test scenarios. In many cases, this assumption does not hold true. For instance, a model will be typically trained under a single environmental condition but at the test time, it can encounter a much more diverse condition. Such discrepancies often occur as acquiring training data that covers diverse environmental conditions can be challenging. This disparity between the training and test distributions, commonly referred to as the domain shift deteriorates the detector’s performance. In the literature, various methods have been employed to mitigate the domain shift issue. One approach involves unsupervised domain adaptation techniques, where the model is adapted to perform well on the target domain by leveraging unlabeled images from that do- main. Another avenue of research is domain generalization, which aims to train models that can generalize effectively across multiple target domains without direct access to data in that particular domain. In this thesis, we propose unsupervised domain adaptation and domain generalization meth- ods to alleviate domain shift. First, we introduce an attention-based module to obtain local object regions in the single-stage detectors. Here we show the efficacy of a gradual transition from global image features adaptation to local region adaptation. While this work mainly focuses on appearance shifts due to illumination or weather change, in our second work, we show that the gap introduced due to differences in the camera setup and parameters is non-negligible, as well. Hence, we propose a method to learn a set of homographies that allow us to learn robust features to bring two domains closer under such shifts. Both of these works have access to unlabelled data in the target domain, but sometimes even unlabeled data is scarce. To tackle this, in our third work, we propose a domain generalization method by leveraging image and text-aligned feature embeddings. We estimate the visual features of the target domain based on the textual prompt describing the domain.