We carried out first-principles calculations within density-functional theory to investigate the structural, electronic, and magnetic properties of boron-nitride (BN) honeycomb structure functionalized by adatom adsorption, as well as by the substitution of foreign atoms for B and N atoms. For periodic high-density coverage, most of 3d transition metal atoms and some of group 3A, 4A, and 6A elements are adsorbed with significant binding energy and modify the electronic structure of bare BN monolayer. While bare BN monolayer is nonmagnetic, wide band-gap semiconductor, at high coverage of specific adatoms it can achieve magnetic metallic, even half-metallic ground states. At low coverage, the bands associated with adsorbed atoms are flat and the band structure of parent BN is not affected significantly. Therefore, adatoms and substitution of foreign atoms at low coverage are taken to be the representative of impurity atoms yielding localized states in the band gap and resonance states in the band continua. Notably, the substitution of C for B and N yield donorlike and acceptorlike magnetic states in the band gap. Localized impurity states occurring in the gap give rise to interesting properties for electronic and optical application of the single-layer BN honeycomb structure. © 2010 The American Physical Society.