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  
7. Sentence-Level Alignment Methods  
8. Document-Level Alignment Models  
9. From Bilingual to Multilingual Training  
10. Evaluation  
11. Applications  
12. General Challenges and Future Directions  
13. Conclusion