In 1990, VAERS (Vaccine Adverse Event Reporting System) was established as a joint resource managed by the FDA and the CDC. It is not the only reporting system of its kind. At the very least, there is the Defense Medical Epidemiology Database (DMED), an epidemiological tracking database maintained by the Military Health Service. One important difference between VAERS and DMED is that VAERS is open to reporting by public whereas DMED is only available to the personnel operating within the DoD's military system (and possibly its contractors). So DMED is clearly a valuable resource but we will only be focusing on the VAERS for the purpose of this article.
Since VAERS' founding underreporting in it was a concern. In 1997 the National Academy of Sceinces held a forum dedicated to addressing this problem. 10 years later, in 2007-2010 a study by the Harvard Pilgrim Health Care concluded that less than 1% of vaccine adverse effects were reported to VAERS.
Reasons for that are not clear. I would speculate they have to do with lacking correlation capabilities of many medical offices, interpersonal communication breakdowns, industry pressure and a number of other factors. But the findings, if anywhere close to accurate, were quite alarming, regardless of the cause.
References
Electronic Support for Public Health–Vaccine Adverse
Event Reporting System (ESP:VAERS)
Harvard-Pilgrim VAERS study document, Agency for Healthcare Research and Quality, 2007-2010
Agency for Healthcare Research and Quality
Vaccine Safety Forum: Summaries of Two Workshops
National Academy of Sciences, 1997