1 INTRODUCTION  
2 BACKGROUND - DEFINITIONS AND ASSUMPTIONS  
2.1 Causality and SCMs  
2.2 Graphical Models  
2.3 The Markov Assumption, $d$-Separation, and $d$-Faithfulness  
2.4 Markov Equivalence Class (MEC) and Completed Partially Directed Acyclic Graphs (CPDAGs)  
2.5 Assumption: Sufficiency  
2.6 Acyclic Directed Mixed Graphs (AGMGs) and Maximal Ancestral Graphs (MAGs) and $m$-separation  
2.7 Partial Ancestral Graphs (PAGs)  
2.8 Other Definitions and Assumptions  
3 STRUCTURE DISCOVERY METHODS  
3.1 Constraint-Based and Score-Based Approaches  
3.2 Exploiting Structural Asymmetries  
3.3 Interventions and Adjustment Sets  
3.4 Causality Over Time  
3.5 Evaluation Metrics  
4 COMBINATORIC/SEARCH BASED APPROACHES  
5 CONTINUOUS OPTIMIZATION BASED APPROACHES  
6 SUMMARY AND DISCUSSION  
6.1 Opportunities and Future Directions  
6.2 The Causal Leap