Single-cell analyses of transcript and protein expression profiles-more precisely, single-cell resolution analysis of molecular profiles of cell populations-have now entered the center stage with widespread applications of single-cell qPCR, single-cell RNA-Seq and CyTOF. These high-dimensional population snapshot techniques are complemented by low-dimensional time-resolved, microscopy-based monitoring methods. Both fronts of advance have exposed a rich heterogeneity of cell states within uniform cell populations in many biological contexts, producing a new kind of data that has triggered computational analysis methods for data visualization, dimensionality reduction, and cluster (subpopulation) identification. The next step is now to go beyond collecting data and correlating data points: to connect the dots, that is, to understand what actually underlies the identified data patterns. This entails interpreting the 'clouds of points' in state space as a manifestation of the underlying molecular regulatory network. In that way control of cell state dynamics can be formalized as a quasi-potential landscape, as first proposed by Waddington. We summarize key methods of data acquisition and computational analysis and explain the principles that link the single-cell resolution measurements to dynamical systems theory.