Two-dimensional (2D) materials of atomic thickness have emerged as nano-building blocks to develop high-performance separation membranes that feature unique nanopores and/or nanochannels. These 2D-material membranes exhibit extraordinary permeation properties, opening a new avenue to ultra-fast and highly selective membranes for water and gas separation. Summarized in this Minireview are the latest ground-breaking studies in 2D-material membranes as nanosheet and laminar membranes, with a focus on starting materials, nanostructures, and transport properties. Challenges and future directions of 2D-material membranes for wide implementation are discussed briefly.