High voltage systems operated in vacuum require insulating materials to maintain spacing between conductors held at different potentials, and may be used to maintain a nonconductive vacuum boundary. Traditional vacuum insulators generally consist of a single material, but insulating structures composed of alternating layers of dielectric and metal can also be built. These "high-gradient insulators" have been experimentally shown to withstand higher voltage gradients than comparable conventional insulators. As a result, they have application to a wide range of high-voltage vacuum systems where compact size is important. This paper describes ongoing research on these structures, as well as the current theoretical understanding driving this work.