Abstract Spatial RNA-sequencing has emerged as a revolutionary tool that allows us to address scientific questions that were elusive just a few years ago. Specifically, the spatial RNA-sequencing technology has the potential to revolutionize studies of tissue structure and function in health and disease. However, much of the potential has yet to be realized as statistical methods to analyze spatial RNA-seq data are lacking. For many types of analyses, the methods currently in use obscure and, in some cases, distort biological signals. A number of statistical and computational challenges must be addressed to prevent inaccurate conclusions, and to optimize novel discovery. This proposal addresses those challenges. In particular, while the technology is powerful, it is not without error; and considerable contamination exists in spatial RNA-seq data. We propose methods to remove this contamination and thereby ensure robust and accurate downstream inference. We also propose statistical methods to adjust for technical variability induced by differences in sequencing depth. By reducing technical variability, these methods will improve the power with which signals of interest can be studied. Finally, we propose methods for characterizing changes in the dependence structure of sets of genes. These types of methods are required to improve our understanding of how coordinated changes in genes affect tissue structure and function in health and disease. Taken together, successful completion of this project will help to ensure that maximal information is obtained from powerful spatial RNA-seq experiments.