In this review paper I concentrate exclusively on the multiple periodic RR Lyrae stars and I do not wish to discuss the general problems of cluster variables. There are some excellent review papers on them (e.g. Preston, 1964).
The majority of the RR Lyrae stars repeat their light curves from cycle to cycle with astonishing regularity. It was, however, discovered already in the early days of variable star research that some of them showed conspicuous changes in the height of maxima of their light curve and simultaneously the time of maxima could not be fitted in by a linear formula.