In this talk I will describe our recent ideas of how to engineer nanostructures that generate topological transport of vibrations. These include situations with explicit time-reversal symmetry breaking (via an optical field with optical vorticity) as well as with time-reversal symmetry intact. In the latter case, I will show how the snowflake phononic crystal, first invented for the purposes of optomechanics, provides an ideal platform in which to implement both pseudomagnetic fields for vibrations as well as a topological insulator. Pseudomagnetic fields for sound at the nanoscale Christian Brendel, Vittorio Peano, Oskar Painter, and Florian Marquardt, Proceedings of the National Academy of Sciences (PNAS) 114, E3390–E3395 (2017) Snowflake Topological Insulator for Sound Waves Christian Brendel, Vittorio Peano, Oskar Painter, and Florian Marquardt, arXiv:1701.06330 (2017) Topological Phases of Sound and Light Vittorio Peano, Christian Brendel, Michael Schmidt, and Florian Marquardt, Phys. Rev. X 5, 031011 (2015)