Two-dimensional isotropic fluids can possess an anomalous part of the viscous stress tensor known as odd or Hall viscosity. This peculiar viscosity does not lead to any dissipation in the fluid. Examples of fluids with odd viscosity include rotating superfluids, plasmas in magnetic fields, quantum Hall fluids, and chiral active fluids. I will describe some manifestations of the odd viscosity. In particular, I will focus on surface waves propagating along the boundaries of such fluids. I will also present a variational principle and the corresponding Hamiltonian structure for fluid dynamics with odd viscosity.