The goal of dynamic causal modelling (DCM) of neuroimaging data is to study experimentally induced changes in functional integration among brain regions. This requires (i) biophysically plausible and physiologically interpretable models of neuronal network dynamics that can predict distributed brain responses to experimental stimuli and (ii) efficient statistical methods for parameter estimation and model comparison. These two key components of DCM have been the focus of more than thirty methodological articles since the seminal work of Friston and colleagues published in 2003. In this paper, we provide a critical review of the current state-of-the-art of DCM. We inspect the properties of DCM in relation to the most common neuroimaging modalities (fMRI and EEG/MEG) and the specificity of inference on neural systems that can be made from these data. We then discuss both the plausibility of the underlying biophysical models and the robustness of the statistical inversion techniques. Finally, we discuss potential extensions of the current DCM framework, such as stochastic DCMs, plastic DCMs and field DCMs.