  I summarize what is known about the Euler-Heisenberg Lagrangian and its
multiloop corrections for scalar and spinor QED, in various types of constant
fields, and in various dimensions. Particular attention is given to the
asymptotic properties of the weak-field expansion of the Lagrangian, which via
Borel summation is related to Schwinger pair-creation, and the status of the
"exponentiation conjecture" for the imaginary part of the Euler-Heisenberg to
all loop orders.
