  Although the equations of motion for the Neveu-Schwarz (NS) and Ramond (R)
sectors of open superstring field theory can be covariantly expressed in terms
of one NS and one R string field, picture-changing problems prevent the
construction of an action involving these two string fields. However, a
consistent action can be constructed by dividing the NS and R states into three
string fields which are real, chiral and antichiral.
  The open superstring field theory action includes a WZW-like term for the
real field and holomorphic Chern-Simons-like terms for the chiral and
antichiral fields. Different versions of the action can be constructed with
either manifest d=8 Lorentz covariance or manifest N=1 d=4 super-Poincar\'e
covariance. The lack of a manifestly d=10 Lorentz covariant action is related
to the self-dual five-form in the Type IIB R-R sector.
