Spatial transcriptomics technologies measure RNA expression at thousands of locations in a tissue sample providing information about the spatial distribution of cell types and the spatial variation in gene expression across a tissue. However, these measurements are typically sparse with high rates of missing data. In this talk, I will present algorithms that address data sparsity by modelling spatial correlations between measurements within and across tissue slices. First, our Belayer algorithm describes variation in gene expression in a single slice using a model of a layered tissue that consists of stacked layers with distinct cell type composition, such as found in the brain and skin. We extend this approach to more general tissue geometries using an interpretable deep learning model that derives a one-dimensional coordinate, the isodepth, that models both discontinuous and continuous variation in gene expression. Finally, our PASTE algorithm aligns and integrates spatial transcriptomics data from multiple slices from the same tissue enabling downstream applications such as differential gene expression and 3D reconstruction of tissues. The advantages of these methods will be illustrated on spatial transcriptomics data from multiple tissue types.