Optimal transport for single-cell and spatial omics

High-throughput single-cell profiling provides an unprecedented ability to uncover the molecular states of millions of cells. These technologies are, however, destructive to cells and tissues, raising practical challenges when aiming to track dynamic biological processes. As the same cell cannot be observed at multiple time points, as it changes in time and space in response to a stimulus or perturbation, these large-scale measurements only produce unaligned data sets. In this Primer, we show how such challenges can be effectively addressed using the unifying framework of optimal transport theory and tackled using the many algorithms that have been proposed for the range of scenarios of key interest in computational biology. We further review recent advances integrating optimal transport and deep learning that allow forecasting heterogeneous cellular dynamics and behaviour, crucial in particular for pressing problems in personalized medicine.