I am aware of three reputable causal inference frameworks:
1. Judea Pearl's framework, which dominates in CS and AI circles
2. Neyman-Rubin causal model: https://en.wikipedia.org/wiki/Rubin_causal_model
3. Structural equation modelling: https://en.wikipedia.org/wiki/Structural_equation_modeling
None of them would acknowledge each other, but I believe the underlying methodology is the same/similar. :-)
It's good to see that it is becoming more accepted, especially in Medicine, as it will give more, potentially life-saving, information to make decisions.
In Social Sciences, on the other hand, causal inference is being completely willfully ignored. Why? Causal inference is an obstacle to making a preconceived conclusions based on pure correlations: something correlates with something, therefore ... invest large sums of money, change laws in our favor, etc... This works for both sides. Sadly, I don't think this could be fixed.