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Deep learning for cross-subject EEG decoding is hindered by high inter-subject variability, which introduces a severe domain shift between training and unseen test subjects. This survey presents a comprehensive review of deep learning methodologies specifically engineered to address this cross-subject generalization challenge. To ground this analysis, we formalize the cross-subject setting as a multi-source domain problem and delineate the rigorous, subject-independent evaluation protocols required for valid assessment. Central to this survey is a systematic taxonomy of the current literature into discrete methodological families, including feature alignment, adversarial learning, feature disentanglement, and contrastive learning. We conclude by examining three critical elements for advancing robust, real-world decoding: the theoretical limitations of current methodologies, the structural value of subject identity, and the emergence of EEG foundation models.