The current status of the experimental searches for rare alpha and beta decays is reviewed. Several interesting observations of alpha and beta decays, previously unseen due to their large half-lives ($10^{15} - 10^{20}$ yr), have been achieved during the last years thanks to the improvements in the experimental techniques and to the underground locations of experiments that allows to suppress backgrounds. In particular, the list includes first observations of alpha decays of $^{151}$Eu, $^{180}$W (both to the ground state of the daughter nuclei), $^{190}$Pt (to excited state of the daughter nucleus), $^{209}$Bi (to the ground and excited states of the daughter nucleus). The isotope $^{209}$Bi has the longest known half-life of $T_{1/2} approx 10^{19}$ yr relatively to alpha decay. The beta decay of $^{115}$In to the first excited state of $^{115}$Sn (E$_{exc} = 497.334$ keV), recently observed for the first time, has the $Q_beta$ value of only $(147 pm 10)$ eV, which is the lowest $Q_beta$ value known to-date. Searches and investigations of other rare alpha and beta decays ($^{48}$Ca, $^{50}$V, $^{96}$Zr, $^{113}$Cd, $^{123}$Te, $^{178m2}$Hf, $^{180m}$Ta and others) are also discussed.
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