Inorganic matter and some ash-forming elements of biomass may cause numerous technological and environmental problems during biomass processing. Therefore, an extended overview of the ash contents and ash-forming elements of biomass and their significance for solid biofuel combustion was conducted based on reference peer-reviewed data plus own investigations. Initially, some general considerations such as current bioenergy situation and different aspects related to biomass use as biofuels, as well as some common issues concerning the main advantages and disadvantages of ash contents and ash-forming elements of biomass are discussed. Then, definition, specification, terminology clarification and composition related to inorganic and mineral matter of biomass and biomass ash (BA) are considered. Further, the contents and concentration/depletion trends of ash (for 532 biomass varieties) and 12 ash-forming elements based on traditional and complete ash analysis of Si, Ca, K, P, Al, Mg, Fe, S, Na and Ti oxides (141 BA varieties) plus elemental Cl (87 BA varieties) and Mn (156 BA varieties) were characterized. The correlations and associations among the ash yields and contents of ash-forming elements of natural biomass (127 biomass and BA varieties) were also identified using the present database. Finally, the origin and significance of ash-forming elements and their associations established in biomass, namely (1) Si - Al - Fe - Ti; (2) Ca - Mg - Mn; and (3) K - P - S - Cl - Na were described and the benefits and obstacles of these associations for biofuel combustion were evaluated. It was found that the high ash yields and contents of some ash-forming elements such as Cl, K, Na, P, S and some other elements with unfavorable modes of element occurrences (chlorides, sulphates, carbonates, oxalates, nitrates and some oxyhydroxides, phosphates and amorphous material) in biomass and BA may provoke the most critical technological and environmental challenges during biomass processing and especially during biomass thermochemical conversion. (C) 2017 Elsevier Ltd. All rights reserved.