1 Introduction  
2 Cross-Lingual Alignment  
2.1 Definitions  
2.2 Measuring Cross-Lingual Alignment  
3 Taxonomy of Alignment Strategies  
3.1 Objectives using Parallel Data  
3.2 Contrastive Learning  
3.3 Modified Pre-Training Schemes  
3.4 Adapter Tuning  
3.5 Data Augmentation  
3.6 Transformation of Representations  
3.7 Tuning with Task Data  
4 What We Do and Don’t Know  
5 Multilingual Generative Models  
5.1 Multilinguality As An Afterthought?  
5.2 Cross-Linguality in Generative Models  
5.3 Where to Align a Generative Model?  
5.4 Evaluation of Multilingual Generation  
6 Conclusions