(A) Band structure ${\overline{\omega }}_{\pm }(\overline{q})$ for for the bulk with a bandgap (grey) connected to edge states (green) with frequencies laying in the bandgap. (B) Localised edge modes of a chiral active fluid in a linear channel. The rotors move with the emerging edge flow. (C) The topologically protected edge modes are unidirectional and robust such that they do not scatter off sharp edges at the boundary, but navigate along the edge. (D) Topologically protected sound modes in a compressible chiral active fluid. The wave is excited at frequencies laying in the band gab at the star symbol and subsequently move unidirectionally along the boundary without scattering off edges. (A, D) Reprinted with permission from [71]. Copyright©2019 the American Physical Society. (B, C) Reprinted with permission from [105]. Copyright©2018 National Academy of Sciences. (E) Cargo (larger particle) transport in a granular chiral active fluid consisting out of vibrational gears aided by odd viscosity and topologically protected edge modes. Reprinted with permission from [61]. Copyright©2021 the American Physical Society.