The theory of graph limits, introduced by Lovász and Szegedy, was extended to several combinatorial structures. In this talk, we focus on permutation sequences and k-dimensional poset sequences. We define convergence for both sequences and present their limit objects. As consequence, the limit objects can be used as models for random permutations and random k-dimensional posets, and can also be used to characterize testable parameters of permutations and posets.