Classes of complex-valued Borel measures that are uniquely determined by their restrictions

The paper is a survey of results on classes of measures on the real axis that are uniquely determined by restrictions to the semi-axis. Connections are discussed between the results and methods in question and the distribution values theory, factorization in the Hardy class $H^\infty$, divisibility of quasipolynomials, and questions of growth and decay of analytic functions.