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I will discuss a theory of formal explainable AI that has emerged over the last few years, which is geared towards explaining the decisions of learned classifiers likes ones based on Bayesian Networks, random forests and some types of neural networks. The theory is based on compiling the input-output behavior of such classifiers into symbolic form and then using sophisticated machinery from symbolic logic to explain decisions. The theory employs newly-introduced, and profound, abstraction operators that distill the essence of an instance (i.e., classifier input) which causes the decision on that instance. Among the implications is an ability to identify minimal aspects of an instance that guarantee the decision, and minimal aspects that must be changed (and in what way) to change the decision. I will illustrate the theory using concrete examples and case studies and also tie these developments to more classical explanations and some widely used approximate explanations.