Chiral active fluids are materials composed of self-spinning rotors that continuously inject energy and angular momentum at the microscale. Out-of-equilibrium fluids with active-rotor constituents have been experimentally realized using nanoscale biomolecular motors, microscale active colloids, or macroscale driven chiral grains. I will discuss how chiral active fluids break both parity and time-reversal symmetries in their steady states, giving rise to a dissipationless linear-response coefficient called odd (equivalently, Hall) viscosity in their constitutive relations. This odd viscosity provides no energy dissipation, but can give rise to a transverse flow – for example within a hypersonic shock. Such a viscosity term has been previously examined in the context of electron fluids subject to a magnetic field. However, only in active fluids does odd viscosity: (i) arise out of equilibrium, (ii) always come accompanied by an antisymmetric stress, and (iii) become ill-defined in the regime in which active rotations are hindered by interactions. I will examine the origins of odd viscosity and suggest how this property may be exploited to build machines powered by active fluids.