From the Congressional Research Service:

More than 200 million Americans have received one or more doses of a Coronavirus Disease 2019
(COVID19) vaccine, along with
billions of people worldwide. The Food and Drug Administrations
(FDAs) emergency use authorizations for the
PfizerBioNTech, Moderna, and Johnson & Johnson
COVID19 vaccines were based on monthslong clinical trials (including safety monitoring) of each
vaccine, involving tens of thousands of participants. These trials
did not identify any safety concerns that
would preclude such authorization. (The
PfizerBioNTech COVID19 vaccine subsequently received full
approval
from FDA.) Postauthorization, the COVID19 vaccines have been subject to safety monitoring
requirements by FDA and the Centers for Disease Control and Prevention (CDC) to detect longterm or
rare adverse health events. (For more information, see
this CRS report.)

Read the full article here >