As methods for measuring spatial gene expression at single-cell resolution become available, there is a need for computational analysis strategies. We present trendsceek, a method based on marked point processes that identifies genes with statistically significant spatial expression trends. trendsceek finds these genes in spatial transcriptomic and sequential fluorescence in situ hybridization data, and also reveals significant gene expression gradients and hot spots in low-dimensional projections of dissociated single-cell RNA-seq data.