This paper aims to summarize the evolution of lunar base concepts over the past approximately half-century. We will discuss the various classes of concepts, the lunar environment as it pertains to structural design, construction, and human habitation. Topics introduced are: The Lunar Surface Environment; Lunar Base Concepts During the Apollo Era; More Recent Concepts for Lunar Structures; Futuristic Concepts and Applications. To understand the various classes of lunar structures for habitation, it is important to explain the key environmental factors that affect human survival on the Moon and affect structural design and construction on the Moon. The key environmental factors are: (i) the surface is in a hard vacuum, and is thus vulnerable to galactic and solar radiation and to micrometeorites, (ii) a shirt-sleeve environment requires an internally-pressurized structure, (iii) suspended fines from the lunar surface can cause severe damage to mechanisms and machines supporting structural operations. Lunar base structural concepts attempt to address the above issues in various ways. To reduce vulnerability to radiation and micrometeorites, surface structures need to be shielded, with the most popular approach being the placement of about 3 meters of regolith on top of the structure. This approach leads to challenging construction procedures, and also makes ingress and egress difficult. Structure maintenance in the presence of an envelope of regolith remains to be addressed. Human habitation requires ways to bring outside light and views into the structure, since long-term habitation in windowless spaces is viewed negatively. The internal pressurization turns out to be the controlling design load for a lunar surface structure, even with 3 meters of regolith on the outside. For inflatable structures, of particular concern is the loss of pressurization. Structural concepts for human habitation on the lunar surface include the "tin can" structure, the inflatable structure, the truss-based structure, the fused-regolith structure, and hybrids. As expected, each class has its advantages and disadvantages. The "tin can" is comparatively easy to build on Earth orbit and transport and land on the Moon, with the disadvantage that it is not easily expandable. A disadvantage of the inflatable concept is the threat of deflation, but an important advantage is that large volumes can be enclosed by the inflatable, and it is easier to transport. The truss-based structure is most similar to Earth structures, and most easily understood in terms of current structural design and construction practice. However, strength requires heavy structural members, not likely to be manufactured on the Moon soon. It is clear that the type of lunar civilization that can evolve depends on the infrastructure that we are capable of building.