This paper introduces the Tasking Control API—an API which allows tools, e.g. debuggers, to control the execution of task-based programming models as for instance OpenMP or OmpSs. However, the design of Tasking Control API is sufficiently generic to be applied to any other programming model for asynchronous task parallelization. We call this debugging approach model-centric debugging as opposed to language-centric debugging. The specification of Tasking Control API follows the spirit of the OpenMP Tools Interface to allow simple interoperability or even a future integration of Tasking Control API into the OpenMP Tools Interface.