  We introduce a general model of trapping for random walks on graphs. We give
the possible scaling limits of these Randomly Trapped Random Walks on $\mathbb
{Z}$. These scaling limits include the well-known fractional kinetics process,
the Fontes-Isopi-Newman singular diffusion as well as a new broad class we call
spatially subordinated Brownian motions. We give sufficient conditions for
convergence and illustrate these on two important examples.
