The paper is an up-to-date survey of the congruence subgroup problem. It contains the statement of Serre's conjecture on the congruence subgroup property for $S$-arithmetic subgroups of simple simply connected groups of $S$-rank $\geq $ 2, and most of the results that confirm it. Besides, some new methods of attacking the congruence subgroup problem are described which provide new examples of groups with the congruence subgroup property.