The present invention relates to curable compositions that include a hydrazide functional material (a) represented by the following Formula (I), For Formula (I): n is 2; independently for each n, x is 0 or 1, y is 0 or 1, provided that the sum of x and y is 1; L1, independently for each n, is selected from a divalent hydrocarbyl group optionally interrupted with at least one of —O— and —S—; L2, independently for each n, is selected from a divalent hydrocarbyl group; and R1, independently for each n, is selected from hydrogen and hydrocarbyl. The curable compositions further include a reactant (b) that has at least two reactive groups that are reactive with and form covalent bonds with the hydrazide groups of the hydrazide functional material (a). The present invention also relates to curable powder coating compositions and curable adhesive compositions.