Data assimilation combines observational information with numerical models taking into account the errors in both the observations and the model. In ensemble data assimilation the errors in the model state are dynamically estimated using an ensemble of model states. Data assimilation is used with coupled models to generate model fields to initialize model predictions, for computing a model state over time as a reanalysis, to optimize model parameters, and to assess model deficiencies. The coupled models simulate different compartments of the Earth system as well as their interactions. For example coupled atmosphere-ocean models like the AWI Climate Model (AWI-CM), simulate the physics in both compartments and fluxes in between then. Data assimilation is used with coupled models to generate model fields to initialize model predictions, for computing a model state over time as a reanalysis, to optimize model parameters, and to assess model deficiencies. Ensemble data assimilation methods can be applied with these model systems, but have a high high computing cost. To allow us to efficiently perform the data assimilation, the parallel data assimilation framework (PDAF) has been developed. I will discuss the application and challenges of coupled ensemble data assimilation on the examples of the data assimilative model system of AWI-CM coupled to PDAF and a coupled ocean-biogeochemical model consistent of the ocean circulation model MITgcm and the ecosystem model REcoM2.