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The combustion phenomenon is characterized by rapid self-sustaining reactions, which can occur in the solid, liquid, or gas phase. Specific types of these reactions are used to produce valuable materials by different combustion synthesis (CS) routes. In this article, all three CS approaches, i.e. solid-phase, solution, and gas-phase flame, are reviewed to demonstrate their attractiveness for fabrication of zero-, one-, two-, and three-dimensional nanostructures of a large variety of inorganic compounds. The review involves five sections. First, a brief classification of combustion synthesis methods is given along with the scope of the article. Second, the state of art in the field of solid-phase combustion synthesis is described. Special attention is paid to the relationships between combustion parameters and structure/properties of the produced nanomaterials. The third and fourth sections describe details for controlling material structures through solution combustion synthesis and gas-phase flame synthesis, respectively. A variety of properties (e.g., thermal, electronic, electrochemical, and catalytic) associated with different types of CS nanoscale materials are discussed. The conclusion focuses on the most promising directions for future research in the field of advanced nanomaterial combustion synthesis. [ABSTRACT FROM AUTHOR]