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In this tutorial, we provide a comprehensive survey of the exciting recent work on cutting-edge weakly-supervised and unsupervised cross-lingual word representations. After providing a brief history of supervised cross-lingual word representations, we focus on: 1) how to induce weakly-supervised and unsupervised cross-lingual word representations in truly resource-poor settings where bilingual supervision cannot be guaranteed; 2) critical examinations of different training conditions and requirements under which unsupervised algorithms can and cannot work effectively; 3) more robust methods for distant language pairs that can mitigate instability issues and low performance for distant language pairs; 4) how to comprehensively evaluate such representations; and 5) diverse applications that benefit from cross-lingual word representations (e.g., MT, dialogue, cross-lingual sequence labeling and structured prediction applications, cross-lingual IR).