An important step in the exploration and colonization of the solar system is to build a permanently inhabited base on the Moon. The lunar environment is stark and hostile to unprotected humans. Structures are needed that protect the inhabitants from vacuum, radiation, extreme temperatures, dust, and meteoroids. Transporting the necessary construction materials from Earth is extremely expensive. Fortunately, lunar structures can be built utilizing indigenous materials. The locally available materials include lunar regolith, cast regolith, glass and glass composites, metals and concrete. Their mechanical properties are summarized and their suitability for lunar construction is evaluated. The most promising materials are cast regolith and lunar glass. Several lunar bases concepts utilizing indigenous materials are described and evaluated. Precast modules and large cast in place structures can be fabricated from lunar concrete. Large cylindrical modules, curved and flat panels and arches cast from lunar regolith are also feasible. A tied arch system is considered very promising because of its structural efficiency.