In this talk we discuss how rigorous relations between causal models may be defined and quantitatively evaluated. We will start with a quick introduction to the popular formalism of structural causal models. Next, we will review alternative proposals for expressing relations of abstractions between these models. We will then focus on one particular framework, and show how a notion of abstraction error can be introduced in this setup. Finally, we will discuss some of the limitations of this measure, and how alternative measures of error may be developed in order to capture different aspects of abstraction and fit different aims. We will conclude with a few considerations about possible future developments of this theory of abstraction.