The survey is based on the material published in the Universal Algebra section of Referativnyĭ Zhurnal Matematika in the period from 1976 till 1988; only the results and the directions are included that were not covered by several similar surveys and are the most promising ones according to the author's opinion. There are 69 references selected from almost two thousand. The survey is organized in the following sections: Lattices of (quasi-) varieties; (quasi-) varieties satisfying finiteness conditions; Mal'tsev conditions; various properties of classes of algebras; congruences and relations on algebras; homomorphisms; basic constructions; subalgebra systems; clones of operations; interpolation and completeness; algebras of polynomials, affine algebras and algebras with large automorphism groups; extensions, solutions of systems of equations, equational compactness; computer universal algebra.