 Carbon nanotubes, CNTs, are nanoscale cylinders of graphene with exceptional properties such as high mechanical strength, high aspect ratio, and large specific surface area. To exploit these properties for membranes, macroscopic structures need to be designed with controlled porosity and pore size. This manuscript reviews recent progress on two such structures. CNT-bucky papers, a nonwoven, paper-like structure of randomly entangled CNTs, and two isoporous CNT membranes, where the hollow CNT interior acts as a membrane pore. The construction of these two types of membranes will be discussed, characterization and permeance results compared, and some promising applications presented. This article was authored by Stephen Gray, Stephen Hawkins, Mikhail Duke, and others.