The study of chromatin accessibility and DNA methylation have been fundamentally important to the understanding of gene regulation and disease. I developed methyl-ATAC-seq to query the relationship between DNA methylation and accessibility at transposase-hypersensitive chromatin, and to characterize sites of methylation-dependent accessibility in human colorectal tumor cells. Furthermore, I have performed single-cell combinatorial indexing assay for transposase accessible chromatin using sequencing (sci-ATAC-seq) to characterize the changes in cellular heterogeneity and chromatin accessibility in the cortices of Ts65Dn Down syndrome model mice. Using sci-ATAC-seq I identified 26 distinct cell-types in the cortex; I found broad changes in cell-type distribution of varying severity, including a substantial increase in abundance of several classes of interneurons corresponding to a decrease in excitatory neuron abundance. These efforts provide novel tools for analyzing chromatin states and a high-resolution assay of cellular changes that accompany Down syndrome.