  After recalling the definition of Zilber fields, and the main conjecture
behind them, we prove that Zilber fields of cardinality up to the continuum
have involutions, i.e., automorphisms of order two analogous to complex
conjugation on (C,exp). Moreover, we also prove that for continuum cardinality
there is an involution whose fixed field, as a real closed field, is isomorphic
to the field of real numbers, and such that the kernel is exactly 2{\pi}iZ,
answering a question of Zilber, Kirby, Macintyre and Onshuus.
  The proof is obtained with an explicit construction of a Zilber field with
the required properties. As further applications of this technique, we also
classify the exponential subfields of Zilber fields, and we produce some
exponential fields with involutions such that the exponential function is
order-preserving, or even continuous, and all of the axioms of Zilber fields
are satisfied except for the strong exponential-algebraic closure, which gets
replaced by some weaker axioms.
