  In this report I will briefly review the motivation and history of double
beta decay search since the first consideration of two neutrino process
(2$\beta(2\nu)$) by Maria Goeppert-Mayer in 1935. The first experiments on
search for double beta decay in the late of 1940's and beginning of 1950's are
considered. It is underlined that for the first time the 2$\beta(2\nu)$ decay
has been registered in geochemical experiment with $^{130}$Te in 1950. In
direct (counter) experiment this type of decay for the first time has been
registered in $^{82}$Se by Michael Moe's group in 1987. Now two neutrino double
beta decay has been recorded for 10 nuclei ($^{48}$Ca, $^{76}$Ge, $^{82}$Se,
$^{96}$Zr, $^{100}$Mo, $^{116}$Cd, $^{128}$Te, $^{130}$Te, $^{150}$Nd,
$^{238}$U). In addition, the 2$\beta(2\nu)$ decay of $^{100}$Mo and $^{150}$Nd
to the 0$^+_1$ excited state of the daughter nucleus has been observed and the
ECEC(2$\nu$) process in $^{130}$Ba was observed too. As to neutrinoless double
beta decay (2$\beta(0\nu)$) this process has not yet been registered. In the
review results of the most sensitive experiments (Heidelberg-Moscow, IGEX,
CUORICINO, NEMO-3) are discussed and conservative upper limits on effective
Majorana neutrino mass and the coupling constant of the Majoron to the neutrino
are established as $\langle m_{\nu} \rangle < 0.75$ eV and $\langle g_{ee}
\rangle < 1.9 \cdot 10^{-4}$, respectively.
  The next-generation experiments, where the mass of the isotopes being studied
will be as grand as 100 to 1000 kg, are discussed. These experiments will have
started within a few years. In all probability, they will make it possible to
reach the sensitivity to the neutrino mass at a level of 0.01 to 0.1 eV.
