The survey is devoted to certain current problems in general combinatorial mathematics. The contemporary state-of-the-art of the theory of permanents, questions on the existence and the enumeration of matrices with nonnegative elements, and a number of problems connected with latin rectangles (enumeration, problem of completing a latin square, equidistant arrays) are examined. The main directions in combinatorial theory in connection with selection problems also are analyzed: matroid theory, transversals, extremal problems (coverings, depth of a matrix, Sperner families). Principal attention is paid to the papers reviewed in Referativnyi Zhurnal “Matematika” during 1975–1979.