Accurate and robust detection of multi-class objects in optical remote sensing images is essential to many real-world applications such as urban planning, traffic control, searching and rescuing, etc. However, state-of-the-art object detection techniques designed for images captured using ground-level sensors usually experience a sharp performance drop when directly applied to remote sensing images, largely due to the object appearance differences in remote sensing images in term of sparse texture, low contrast, arbitrary orientations, large scale variations, etc. This paper presents a novel object detection network (CAD-Net) that exploits attention-modulated features as well as global and local contexts to address the new challenges in detecting objects from remote sensing images. The proposed CAD-Net learns global and local contexts of objects by capturing their correlations with the global scene (at scene-level) and the local neighboring objects or features (at object-level), respectively. In addition, it designs a spatial-and-scale-aware attention module that guides the network to focus on more informative regions and features as well as more appropriate feature scales. Experiments over two publicly available object detection datasets for remote sensing images demonstrate that the proposed CAD-Net achieves superior detection performance. The implementation codes will be made publicly available for facilitating future researches.