Intervertebral discs (IVDs) are small joints that lie between adjacent vertebrae. The localization and segmentation of IVDs are important for spine disease diagnosis and measurement quantification. However, manual annotation is time-consuming and error-prone with limited reproducibility, particularly for volumetric data. In this work, our goal is to develop an automatic and accurate method based on fully convolutional networks (FCN) for the localization and segmentation of IVDs from multi-modality 3D MR data. Compared with single modality data, multi-modality MR images provide complementary contextual information, which contributes to better recognition performance. However, how to effectively integrate such multi-modality information to generate accurate segmentation results remains to be further explored. In this paper, we present a novel multi-scale and modality dropout learning framework to locate and segment IVDs from four-modality MR images. First, we design a 3D multi-scale context fully convolutional network, which processes the input data in multiple scales of context and then merges the high-level features to enhance the representation capability of the network for handling the scale variation of anatomical structures. Second, to harness the complementary information from different modalities, we present a random modality voxel dropout strategy which alleviates the co-adaption issue and increases the discriminative capability of the network. Our method achieved the 1st place in the MICCAI challenge on automatic localization and segmentation of IVDs from multi-modality MR images, with a mean segmentation Dice coefficient of 91.2% and a mean localization error of 0.62 mm. We further conduct extensive experiments on the extended dataset to validate our method. We demonstrate that the proposed modality dropout strategy with multi-modality images as contextual information improved the segmentation accuracy significantly. Furthermore, experiments conducted on extended data collected from two different time points demonstrate the efficacy of our method on tracking the morphological changes in a longitudinal study.