An outstanding challenge in neuroscience is to develop theoretically grounded and practically applicable quantitative measures that are sensitive to conscious level. Such measures should be high for vivid alert conscious wakefulness, and low for unconscious states such as dreamless sleep, coma and general anaesthesia. Here, we describe recent progress in the development of measures of dynamical complexity, in particular causal density and integrated information. These and similar measures capture in different ways the extent to which a system's dynamics are simultaneously differentiated and integrated. Because conscious scenes are distinguished by the same dynamical features, these measures are therefore good candidates for reflecting conscious level. After reviewing the theoretical background, we present new simulation results demonstrating similarities and differences between the measures, and we discuss remaining challenges in the practical application of the measures to empirically obtained data.