We will focus on stochastic processes which are self-similar, have stationary increments and whose finite-dimensional distributions are symmetric $\alpha$-stable. It is known that, in the Gaussian case $\alpha=2$, there is only one self-similar process with stationary increments, the so-called fractional Brownian motion. In contrast, in the non-Gaussian stable case $\alpha<2$, there are infinitely many different self-similar stationary increments processes. We will discuss some recent results on a classification of such processes obtained by relating them to deterministic flows.