Bicontinuous mesophases are mesoporous structures that divide space into several interpenetrating, continuously connected volumes. The length scales of the pores are typically in the tens of nanometer range, which offers opportunities for the use of these materials in nanoscale fabrication of structural composites or surface-active mesoporous structures. Use of these materials has been limited in the past because they were typically liquid crystals made of surfactant and water. This situation is rapidly changing due to recent successes in making bicontinuous mesophases out of more durable materials, such as polymers or silica, and in fabricating structures with a variety of morphologies. An overview is presented of the structural morphology, energetic considerations, and five different routes of fabrication for bicontinuous mesophases, for example, mesophases made of surfactants and water, block copolymers, polymerizable surfactants, polymerizable fluids in surfactant liquid crystals, and silica.