A BSTRACT  
1 Introduction  
2 OT Algorithms at a Glance  
3 History  
4 Mathematical Formalism  
4.1 Problem Statement  
4.2 Kantorovich Duality  
4.3 Entropic Regularization  
4.4 KL Divergence  
4.5 Wasserstein Barycenters  
5 Computational Challenges  
6 Applications  
6.1 Computer Vision  
6.2 Graphs  
6.3 Neural Architecture Search  
6.4 Document Representation  
6.5 Domain Adaptation  
7 Future Research  
8 Concluding Remarks