  We consider Gaussian subordinated L\'evy fields (GSLFs) that arise by
subordinating L\'evy processes with positive transformations of Gaussian random
fields on some spatial domain $\mathcal{D}\subset \mathbb{R}^d$, $d\geq 1$. The
resulting random fields are distributionally flexible and have in general
discontinuous sample paths. Theoretical investigations of the random fields
include pointwise distributions, possible approximations and their covariance
function. As an application, a random elliptic PDE is considered, where the
constructed random fields occur in the diffusion coefficient. Further, we
present various numerical examples to illustrate our theoretical findings.
