Two-dimensional (2D) crystals, despite their atomic thickness, have long been considered as impermeable membranes to all molecules and atoms under ambient conditions: even the smallest of atoms, hydrogen, is expected to take billions of years to penetrate the 2D lattice covered with dense electron clouds. Recently it has been found that monolayer graphene, hexagonal boron nitride, and some other one-atom-thick crystals are highly permeable to protons, raising fundamental questions about the details of the transport process. In this Perspective, we review the mechanism of proton transport through 2D crystals and the related room-temperature quantum effects; the potential applications of 2D membranes in proton-related separation and sieving techniques, including proton exchange membranes and hydrogen isotope separation; and factors that enhance proton permeation and in turn influence 2D membrane design.