Time-to-pregnancy(TTP), the duration that a couple waits from initiating attempts to conceive until conception occurs, is regarded as one of the direct measures of natural fecundity. Statistical tools for designing and analysing TTP studies belong to the general area of survival analysis, but several special features have been developed: it is customary to work in discrete time, and random heterogeneity between couples has always played a prominent role. This review works on this background with focus on how to perform valid analyses, under various prospective, retrospective and cross-sectional sampling frames. We illustrate using examples from our own experience.