  Using the bosonic supercurrent (or covariant lattice) formalism, we review
how to compute scattering amplitudes in asymmetric orbifold string models. This
method is particularly useful for calculating scattering of multiple
asymmetrically twisted string states, where the twisted states are rewritten as
ordinary momentum states. We show how to reconstruct some of the 3-family grand
unified string models in this formalism, and identify the quantum numbers of
the massless states in their spectra. The discrete symmetries of these models
are rather intricate. The superpotentials for the 3-family E_6 model and a
closely related SO(10) model are discussed in some detail. The forms of the
superpotentials of the two 3-family SU(6) models (with asymptotically-free
hidden sectors SU(3) and SU(2) \otimes SU(2)) are also presented.
