In the year 2000, Judea Pearl published Causality.  What controversies surround this work?  What are its major criticisms?
Some authors dislike Pearl's focus on the directed acyclic graph (DAG) as the way in which to view causality.  Pearl essentially argues that any causal system can be considered as a non-parametric structural equation model (NPSEM), in which the value of each node is taken as a function of its parents and some individual error term; the error terms between different nodes may in general be correlated, to represent common causes.
Cartwright's book Hunting Causes and Using Them, for example, gives an example involving a car engine, which she claims cannot be modelled in the NPSEM framework.  Pearl disputes this in his review of Cartwright's book.
Others caution that the use of DAGs can be misleading, in that the arrows lend an apparent authority to a chosen model as having causal implications, when this may not be the case at all.  See Dawid's Beware of the DAG.  For example, the three DAGs $A \rightarrow B \rightarrow C$, $A \leftarrow B \rightarrow C$ and $A \leftarrow B \leftarrow C$ all induce the same probabilistic model under Pearl's d-separation criterion, which is that A is independent of C given B.  They are therefore indistinguishable based upon observational data.
However they have quite different causal interpretations, so if we wish to learn about the causal relationships here we would need more than simply observational data, whether that be the results of interventional experiments, prior information about the system, or something else.
