Owing to unusual thermal, mechanical, electronic and transport properties, beryllium monoxide BeO belongs to the most technically promising ceramic materials for electronic, nuclear, aerospace, electrotechnical, and other advanced applications. A lot of interesting physical properties of metal-oxide systems, which are not characteristic of the pure compounds, may arise in the same materials containing impurities or other point defects. Computational ab initio theory is an effective approach in the determination of structural, magnetic, optical, dielectric and superconducting properties of materials, as it involves no a priori assumptions about the electronic structure and atomic interactions, and creates new opportunities for design of new materials with promising properties. This review focuses on the results of systematic ab initio simulations of the influence of point defects (s, p, d impurities, as well as anionic and cationic lattice vacancies) on the electronic and magnetic properties of BeO. The new effects such as impurity-induced magnetism, vacancyinduced magnetism and mixed (impurity+vacancy)-induced magnetism of BeO are discussed in detail. Finally, the theoretical models of predicted BeO nanotubes and the influence of point defects on their properties are considered.