Atomically thin layers including pores, their method of manufacture, and their use are disclosed. In some embodiments, pores may be formed in an atomically thin layer by growing the atomically thin layer on exposed portions of a substrate that includes islands comprising a material that is different than the material of the substrate. In some embodiments, pores and/or defects may be formed in an atomically thin layer by employing growth conditions that promote the formation of defects and/or pores. In certain embodiments, pores and/or defects may be etched to enlarge their size.