Among various kinds of radical reactions, the addition of carbon-centered radicals to unsaturated bonds represents a powerful tool for the construction of different C-C and C-X (X = N, O, S, etc.) bonds, in which typically applied unsaturated bonds include alkenes, alkynes, imines, carbonyls, and even thiocarbonyls. When C=X bonds are utilized as the radical acceptors, reactions usually occur at the carbon position to generate a heteroatom radical, during which C-C coupling products are formed. This reaction mode has dominated this field for several decades. However, there is also another unconventional type of radical addition mode, in which carbon-centered radicals attack the heteroatom position of C=X bonds to generate carbon radicals, during which selective C-X bond formation is achieved. This reaction mode demonstrates an effective method for the construction of different C-X bonds, such as C-O, C-N, and C-S bonds. This Focus Review gives an overview of recent advances in this unconventional field.