Development and the associated cellular differentiation are some of the most fundamental processes in biology. Since the early conception of the Waddington landscape, with cells portrayed as rolling down a landscape, understanding these processes has been at the forefront of biology. Progress in tissue regeneration, organoid culture, and cellular reprogramming relies on our ability to unfold cellular decision making and its dynamics. In this thesis, we ask to what extent development follows such landscape. Secondly, we address whether cellular branching points are discrete events. Given the recent surge in single-cell genomics data, we can now address these fundamental questions. To this end, we analyzed two large-scale single-cell RNAseq time course datasets from vertebrate embryogenesis in zebrafish. From the Waddington analogy, we expect the cell-to-cell correlation to increase across development as cells specialize. Our analysis does not show a linear trend, but rather, that cell-to-cell variability is lowest during gastrulation. Interestingly, the two different datasets from two different laboratories display a qualitatively similar trend, providing internal consistency of our analysis. To uncover the branchpoint dynamics, we extended our analysis to include computations of gene-to-gene correlations. It has been shown, using PCR data, that the transition index, the ratio between cell-to-cell and gene-to-gene correlations, displays a peak during such branchpoints, suggesting discrete transitions. To this end, we tracked individual developmental trajectories, and characterized both correlations, enabling computation of the transition index. However, the cell-to-cell correlation and gene-to-gene correlation did not follow a generic inverse relationship, as previously suggested. No unique signal corresponding to the branchpoints could, thus, be detected. Therefore, our analysis does not support the view that branchpoints during vertebrate embryogenesis are discrete, well-defined transition events. In conclusion, this first large-scale single-cell based analysis of time-resolved developmental data does not support a downhill rolling ball notion where cells decide their fate at discrete transition points. The temporal organization of an undulating developmental landscape appears to be more complex than initially conceptualized by Waddington. Therefore, it is of paramount interest to extend this type of analysis to other systems and to develop techniques to compute such landscape in a data-driven manner.