The emerging single-cell and spatial genomics techniques allow us to elucidate the governing rules of multicellular systems with unprecedented resolution and depth. These datasets are often high-dimensional, complex, and heterogeneous. Mathematical tools are needed to extract biological insights from such data. In this talk, we will discuss several mathematical and machine learning methods for exploring the tissue structures, temporal signatures, and cell-cell communication processes on single-cell and spatial genomics data. We will also discuss supervised optimal transport which is motivated by these biological applications where application-induced constraints are enforced in the optimal transport problem.