The subject of this work is periods in time series of the radioactive decay fluctuations. The presence of such periods suggests the possibility of a certain external influence on the parameters of radioactive decay. The evolution of views on the possibility of such an influences are briefly reviewed. A number of stages are considered, each of which expresses a certain circle of ideas, which is realized in it. Experimental works typical for each such stage are considered. The article does not aim to review all works related to the issues discussed in it. This is, first of all, a presentation of ideas that reflect the author's views on the possible mechanisms of the occurrence of periods in the time series of the radioactive decay rate. The links provided in the work are rather illustrative.