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Single-cell RNA sequencing (scRNA-seq) enables the collection of rich phenotypic information of individual cells. During this sequencing process, each cell is destroyed, which poses challenges in the analysis of time-course data of heterogeneous populations since cell trajectories need to be computationally inferred. Standard trajectory inference methods approximate the transcriptional spectrum of all time points combined by a graph, not leveraging information about the time-points at which the profiles were captured. The recently proposed Waddington-OT algorithm instead appeals to the theory of optimal transport to infer probabilistic couplings between different time points. First, as an example of the benefits and drawbacks of these methods, I will show how we applied them to a problem in immunology, revealing previously unknown effector state potential of tissue-resident innate lymphoid cells. Second, I will discuss issues with the sample efficiency of optimal transport methods in high-dimensions and two approaches to overcome this problem. The first approach relies on the notion of the transport rank of a probabilistic coupling and I will provide empirical and theoretical evidence that it can be used to significantly improve the rates of estimation of optimal transport distances and plans. The second approach relies on a wavelet regularization and admits near minimax optimal rates for the estimation of smooth optimal transport maps.