This article is a small survey of the author’s and other mathematicians’ results related to weakly Picard operators in a metric space \((X,d)\) (an operator \(A:X\to X\) is a weakly Picard one if the sequence \((A^nx)\) is convergent for any \(x\in X\) and its limit is a fixed ponit of \(A)\). Applications to differential, integral, and difference equations are also considered. Some open problems are formulated.