So far, the pseudo cross-variogram is primarily used as a tool for the structural analysis of multivariate random fields. Mainly applying recent theoretical results on the pseudo cross-variogram, we use it as a cornerstone in the construction of valid covariance models for multivariate random fields. In particular, we extend known univariate constructions to the multivariate case, and generalize existing multivariate models. Furthermore, we provide a general construction principle for conditionally negative definite matrix-valued kernels, which we use to reinterpret previous modeling proposals.