Comparing Variable Importance Functions (For Modeling)

I’ve been doing some machine learning recently, and one thing that keeps popping up is the need to explain the models and their components. There are a variety of ways to go about explaining model features, but probably the most common approach is to use variable (or feature) importance scores. Unfortunately, computing variable importance scores isn’t as straightforward as one might hope—there are a variety of methodologies! Upon implementation, I came to the question “How similar are the variable importance scores calculated using different methodologies?