So far, reports to the CDC of breakthrough infections are exceedingly rare.
Starting May 1, 2021, the CDC transitioned from monitoring all reported vaccine breakthrough cases to focus on identifying and investigating only hospitalized or fatal cases due to any cause.
It is important to note that reported vaccine breakthrough cases will represent an undercount (due to voluntary reporting. However, overall, this data is extremely positive.
CDC COVID Vaccinations Data Tracker: https://covid.cdc.gov/covid-data-tracker/#vaccinations
CDC Breakthrough Cases
Updated: June 2, 2021