Spatial epigenetic mapping of tissues enables the study of gene regulation programs and cellular functions with the dependency on their local tissue environment. Here we outline a complete procedure for two spatial epigenomic profiling methods: spatially resolved genome-wide profiling of histone modifications using in situ cleavage under targets and tagmentation (CUT&Tag) chemistry (spatial-CUT&Tag) and transposase-accessible chromatin sequencing (spatial-ATAC-sequencing) for chromatin accessibility. Both assays utilize in-tissue Tn5 transposition to recognize genomic DNA loci followed by microfluidic deterministic barcoding to incorporate spatial address codes. Furthermore, these two methods do not necessitate prior knowledge of the transcription or epigenetic markers for a given tissue or cell type but permit genome-wide unbiased profiling pixel-by-pixel at the 10 μm pixel size level and single-base resolution. To support the widespread adaptation of these methods, details are provided in five general steps: (1) sample preparation; (2) Tn5 transposition in spatial-ATAC-sequencing or antibody-controlled pA-Tn5 tagmentation in CUT&Tag; (3) library preparation; (4) next-generation sequencing; and (5) data analysis using our customed pipelines available at: https://github.com/dyxmvp/Spatial_ATAC-seq and https://github.com/dyxmvp/spatial-CUT-Tag . The whole procedure can be completed on four samples in 2-3 days. Familiarity with basic molecular biology and bioinformatics skills with access to a high-performance computing environment are required. A rudimentary understanding of pathology and specimen sectioning, as well as deterministic barcoding in tissue-specific skills (e.g., design of a multiparameter barcode panel and creation of microfluidic devices), are also advantageous. In this protocol, we mainly focus on spatial profiling of tissue region-specific epigenetic landscapes in mouse embryos and mouse brains using spatial-ATAC-sequencing and spatial-CUT&Tag, but these methods can be used for other species with no need for species-specific probe design.