We present an effective method to progressively integrate and refine the cross-modality complementarities for RGB-D salient object detection (SOD). The proposed network mainly solves two challenging issues: 1) how to effectively integrate the complementary information from RGB image and its corresponding depth map, and 2) how to adaptively select more saliency-related features. First, we propose a cross-modality feature modulation (cmFM) module to enhance feature representations by taking the depth features as prior, which models the complementary relations of RGB-D data. Second, we propose an adaptive feature selection (AFS) module to select saliency-related features and suppress the inferior ones. The AFS module exploits multi-modality spatial feature fusion with the self-modality and cross-modality interdependencies of channel features are considered. Third, we employ a saliency-guided position-edge attention (sg-PEA) module to encourage our network to focus more on saliency-related regions. The above modules as a whole, called cmMS block, facilitates the refinement of saliency features in a coarse-to-fine fashion. Coupled with a bottom-up inference, the refined saliency features enable accurate and edge-preserving SOD. Extensive experiments demonstrate that our network outperforms state-of-the-art saliency detectors on six popular RGB-D SOD benchmarks.