  A probabilistic model describes a system in its observational state. In many
situations, however, we are interested in the system's response under
interventions. The class of structural causal models provides a language that
allows us to model the behaviour under interventions. It can been taken as a
starting point to answer a plethora of causal questions, including the
identification of causal effects or causal structure learning. In this chapter,
we provide a natural and straight-forward extension of this concept to
dynamical systems, focusing on continuous time models. In particular, we
introduce two types of causal kinetic models that differ in how the randomness
enters into the model: it may either be considered as observational noise or as
systematic driving noise. In both cases, we define interventions and therefore
provide a possible starting point for causal inference. In this sense, the book
chapter provides more questions than answers. The focus of the proposed causal
kinetic models lies on the dynamics themselves rather than corresponding
stationary distributions, for example. We believe that this is beneficial when
the aim is to model the full time evolution of the system and data are measured
at different time points. Under this focus, it is natural to consider
interventions in the differential equations themselves.
