Structural causal models provide a formalism to express causal relations between variables of interest. Models and variables can represent a system at different levels of abstraction, whereby variables and relations may be coarsened and refined according to the need of an agent or a modeller. However, to switch between different levels of abstraction requires evaluating the trade-off between the consistency and the information loss among models at different levels of abstraction. In this paper we introduce a family of interventional measures that an agent or a modeller may use to evaluate such a trade-off. We analyze the properties of these measures, and propose algorithms to evaluate and learn causal abstractions. Finally, we illustrate the flexibility of our setup by empirically showing how different measures and algorithmic choices may lead to different abstractions.