Topological transport of sound waves and vibrations in solids has attracted considerable attention in the past two years. Several approaches have been proposed and some have been demonstrated. However, it remains an outstanding challenge to create platforms for topological transport of phonons at the nanoscale. In this talk, I will describe three possible approaches that we have proposed. In the first, time-reversal is broken explicitly, with the help of an external laser field containing optical vortices. The nontrivial phase pattern of the laser drive is imprinted onto the phonon dynamics via the optomechanical interaction. In the other two approaches, time-reversal symmetry is preserved and no external drive is present. These approaches rest on geometrical modifications of an existing, experimentally proven phononic crystal, the so-called “snowflake crystal”. I will show how that platform can be engineered to produce either pseudomagnetic fields for vibrational waves or a topological insulator. References: "Topological Phases of Sound and Light", Vittorio Peano, Christian Brendel, Michael Schmidt, and Florian Marquardt, Phys. Rev. X 5, 031011 (2015) "Pseudomagnetic fields for sound at the nanoscale", Christian Brendel, Vittorio Peano, Oskar J. Painter, and Florian Marquardt, PNAS 2017, doi:10.1073/pnas.1615503114 "Snowflake Topological Insulator for Sound Waves", Christian Brendel, Vittorio Peano, Oskar Painter, and Florian Marquardt, arXiv:1701.06330 (2017)