The importance and usefulness of crossing is emphasized for both kaon scattering and kaon production reactions. It is argued, and numerically demonstrated for a chiral Lagrangian, that crossing provides powerful, comprehensive constraints which are often neglected in the evaluation of dynamical models. Cross section calculations are presented for two distinct sets of crossing related reactions: (1) K/sup -/p..-->..K/sup -/p, K/sup +/p..-->..K/sup +/p and p-barp..-->..K/sup -/K/sup +/; (2) K/sup -/p..--> gamma lambda..and ..gamma..p..-->..K/sup +/..lambda.. The crossing relations require that the same hadronic Lagrangian, including coupling constants, govern all of these reactions, and results show that different reactions exhibit different sensitivity to coupling constant uncertainty. Because crossed reactions always entail different kinematic regions of the S matrix, it is expected that such sensitivity is not just representative of the current model but rather a general feature that should be exploited when investigating all relativistic theories.