  Recently there has been much progress in building models of gauge mediation,
often with predictions different than those of minimal gauge mediation. Meade,
Seiberg, and Shih have characterized the most general spectrum which can arise
in gauge mediated models. We discuss some of the challenges of building models
of General Gauge Mediation, especially the problem of messenger parity and
issues connected with R symmetry breaking and CP violation. We build a variety
of viable, weakly coupled models which exhibit some or all of the possible low
energy parameters.
