Recent advances in deep learning have led to the development of accurate and efficient models for various computer vision applications such as object classification, semantic segmentation, and object detection. However, learning highly accurate models relies on the availability of datasets with large number of annotated images. Due to this, model performance drops drastically when evaluated on label-scarce datasets having visually distinct images. This issue is commonly referred to as covariate shift or dataset bias. Domain adaptation attempts to address this problem by leveraging domain shift characteristics from labeled data in a related domain when learning a classifier for label-scarce target dataset. There are a plethora of works to adapt object classification and semantic segmentation models to label-scarce target dataset through unsupervised domain adaptation. Considering that object detection is a fundamental task in computer vision, many recent works have recently focused on addressing the domain adaptation issue for object detection as well. In this paper, we provide a brief introduction to the domain adaptation problem for object detection and present an overview of various methods proposed till date for addressing this problem. Furthermore, we highlight strategies proposed for this problem and the associated shortcomings. Subsequently, we identify multiple aspects of the unsupervised domain adaptive detection problem that are most promising for the future research in the area. We believe that this survey shall be valuable to the pattern recognition experts working in the fields of computer vision, biometrics, medical imaging, and autonomous navigation by introducing them to the problem, getting them familiar with the current status of the progress and providing with promising direction for future research.