Abstract: We overview some basic and striking facts concerning the theory of hypercyclic operators (considered to be born in 1982):
1. Hypercyclicity is a purely infinite-dimensional phenomenon: no finite dimensional space supports any hypercyclic operator;
2. It is not easy at all to determine whether a linear operator is hypercyclic. However, the set of hypercyclic operators is dense for the Strong Operator Topology in the algebra of linear and bounded operators;
3. Hypercyclicity is far from being an exotic phenomenon: any infinite-dimensional separable Frechet space supports a hypercyclic operator.