Human enteroviruses are a major cause of neurological and other diseases. More than 100 serotypes are known that exhibit unexplained complex patterns of incidence, from regular cycles to more irregular patterns, and new emergences. Using 15 years of surveillance data from Japan (2000-2014) and a stochastic transmission model with accurate demography, we show that acquired serotype-specific immunity can explain the diverse patterns of 18 of the 20 most common serotypes (including Coxsackieviruses, Echoviruses, and Enterovirus-A71). The remaining two serotypes required a change in viral characteristics, including an increase in pathogenicity for Coxsackievirus-A6, which is consistent with its recent global rise in incidence. On the basis of our findings, we are able to predict outbreaks 2 years ahead of time (2015-2016). These results have implications for the impact of vaccines under development.