1. Introduction  
2. Notation and Terminology  
3. Monolingual Embedding Models  
4. Cross-Lingual Word Embedding Models: Typology  
5. A Brief History of Cross-Lingual Word Representations  
6. Word-Level Alignment Models  
6.1 Word-Level Alignment Methods with Parallel Data  
6.2 Word-Level Alignment Methods with Comparable Data  
7. Sentence-Level Alignment Methods  
7.1 Sentence-Level Methods with Parallel Data  
7.2 Sentence Alignment with Comparable Data  
8. Document-Level Alignment Models  
8.1 Document Alignment with Comparable Data  
9. From Bilingual to Multilingual Training  
9.1 Multilingual Word Embeddings from Word-Level Information  
9.2 Multilingual Word Embeddings from Sentence-Level and Document-Level Information  
10. Evaluation  
10.1 Intrinsic Tasks  
10.2 Extrinsic Tasks  
11. Applications  
11.1 Benchmarks  
12. General Challenges and Future Directions  
13. Conclusion