  Recent observations of gravitational waves from binary mergers of black holes
or neutron stars and the rapid development of ultra-intense lasers lead strong
field physics to a frontier of new physics in the 21st century. Strong gravity
phenomena are most precisely described by general relativity, and lasers that
are described by another most precisely tested quantum electrodynamics (QED)
can be focused into a tiny area in a short period through the chirped pulse
amplification and generate extremely high intensity electromagnetic (EM) fields
beyond the conventional methods. It is physically interesting to study QED
phenomena in curved spacetimes, in which both strong gravitational and
electromagnetic fields play important roles. There are many sources for strong
gravitational and electromagnetic fields in the sky or universe, such highly
magnetized neutron stars, magnetized black holes, and the early universe. We
review quantum field theoretical frameworks for QED both in the Minkowski
spacetime and curved spacetimes, in particular, charged black holes and the
early universe, and discuss the QED physics in strong EM fields, such as the
vacuum polarization and Schwinger pair production and their implications to
astrophysics and cosmology.
