The current status of study on the phase diagram of boron is given from the theoretical viewpoint. Boron is the last elemental crystal whose phase diagram is missing. In the last decade, several new structures of boron allotropes were found, while some were disproven. Presently, even the number of allotropes of boron is uncertain. A simple reason for this is that there are many and complicated structures, and some are minimally different from the others. A theoretical study thus requires very high accuracy. The difficulty, however, is not merely a technical difficulty of computational scale. The physics involved is quite different from what is obtained by band theory, which is the most successful theory of solids. It is only recent that a fundamental problem of metal/insulator has been solved. We come to know that the interrelationships between nonstoichiometry, partially occupied sites, and the balance of intra/inter-icosahedral bonding, which were considered to be uncorrelated properties, inevitably determine the relative stability of various structures. The configuration of the defects in boron crystals is not capricious but there is some correlation among the defects. Many problems were solved on this ground, and contributed to the creation of the phase diagram. However, there are still many unsolved problems and some newly arose. In particular, for the tetragonal phase, sharp discrepancies are present in both experiment and theory. Thus, the problem of tetragonal phase is described in more detail. From the viewpoint of material research, the phase diagram provides the basis for searching new materials. State-of-the-art methods of structural prediction have stimulated researchers’ interest.