Single-cell analyses of transcript and protein expression profiles – more precisely, single-cell resolution analysis of molecular profiles of cell populations – have now entered center stage with the wide application of single-cell qPCR, single-cell RNA-Seq and CytOF. These high-dimensional population snapshots techniques are complemented by low-dimensional time-resolved microscopy-based monitoring methods of individual cells. 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 stimulated a series of computational analysis methods for data visualization, dimensionality reduction, and “cluster” (subpopulation) identification. The next step is to go beyond collecting data and correlating data points with computational analyses: to connect the dots, that is, to understand what actually underlies the identified data patterns. This entails interpreting the “clouds of points”, each representing a cell in state space, and their structure as manifestation of the regulation by the molecular network. This control of cell state dynamics can be formalized as a quasi-potential landscape, as first proposed by Waddington. We summarize not only key methods of data acquisition and computational analysis but also explain the principles that link the single-cell resolution measurements to dynamical systems theory.