RGB-depth (RGB-D) salient object detection (SOD) recently has attracted increasing research interest, and many deep learning methods based on encoder-decoder architectures have emerged. However, most existing RGB-D SOD models conduct explicit and controllable cross-modal feature fusion either in the single encoder or decoder stage, which hardly guarantees sufficient cross-modal fusion ability. To this end, we make the first attempt in addressing RGB-D SOD through 3-D convolutional neural networks. The proposed model, named RD3D, aims at prefusion in the encoder stage and in-depth fusion in the decoder stage to effectively promote the full integration of RGB and depth streams. Specifically, RD3D first conducts prefusion across RGB and depth modalities through a 3-D encoder obtained by inflating 2-D ResNet and later provides in-depth feature fusion by designing a 3-D decoder equipped with rich back-projection paths (RBPPs) for leveraging the extensive aggregation ability of 3-D convolutions. Toward an improved model RD3D+, we propose to disentangle the conventional 3-D convolution into successive spatial and temporal convolutions and, meanwhile, discard unnecessary zero padding. This eventually results in a 2-D convolutional equivalence that facilitates optimization and reduces parameters and computation costs. Thanks to such a progressive-fusion strategy involving both the encoder and the decoder, effective and thorough interactions between the two modalities can be exploited and boost detection accuracy. As an additional boost, we also introduce channel-modality attention and its variant after each path of RBPP to attend to important features. Extensive experiments on seven widely used benchmark datasets demonstrate that RD3D and RD3D+ perform favorably against 14 state-of-the-art RGB-D SOD approaches in terms of five key evaluation metrics. Our code will be made publicly available at https://github.com/PPOLYpubki/RD3D.