I’m going to go against the grain, but no, it does not exist. The fact that so many people think it does has to do with the fact that cognitive bias is extremely common and many studies use retrospective surveys, which are very prone to such biases. Here is the critical review mentioned on wikipedia, which showed that when errors in previous studies were corrected for, the evidence disappeared: A critical review of menstrual synchrony research
From the abstract: “Three errors are inherent in research based on [McClintock’s] model: (1) an implicit assumption that differences between menses onsets of randomly paired subjects vary randomly over consecutive onsets, (2) an incorrect procedure for determining the initial onset absolute difference between subjects, and (3) exclusion of subjects or some onsets of subjects who do not have the number of onsets specified by the research design. All of these errors increase the probability of finding menstrual synchrony in a sample.… Menstrual synchrony is not demonstrated in any of the experiments or studies.” Emphasis mine.
And from the conclusion (sadly behind a pay wall, though if any of you are very interested I may be able to send a copy): “The two experiments of Russell et al. (1980) and Preti et al. (1986) and the three studies of Graham and McGrew (1980), Quadagno et al. (1981), and McClintock (1969, 1971) all have two or three errors that bias their results toward showing higher than expected frequencies of menses onset convergence in their samples. I have demonstrated in all samples, except McClintock’s two samples of pairs, that statistically significant levels of menstrual synchrony are not found when these errors are corrected. A comparable demonstration for McClintock’s samples of pairs is not possible because the documentation of her research is insufficient for correcting errors and conducting revised tests for menstrual synchrony. ”
Emphasis mine.
Also, the phenomenon of human pheromones has never been shown to actually exist.