A growing body empirical literature deals with persistence in innovation. However, there is neither a survey of the development and status of the field nor a clear statement of a theory of persistence which includes a formal model of the dynamics of firm persistence. This paper fills these gaps by first providing a survey of previous studies of persistence, then presenting a theory, based on the evolutionary approach, to explain the choice of firms to innovate persistently, sporadically or not at all, and finally describing a formal model which shows some striking results corroborated by recent empirical evidence.