Active liquids are composed of self-driven microbots that endow the liquid with a unique set of mechanical characteristics. I will present two designs for materials exhibiting topological states: one using periodic confinement of an active liquid and another using a bulk fluid without periodic order. In a periodic lattice, geometry of confinement controls the structure of topological waves. Without periodic order, topological edge waves can arise in a rotating fluid as a result of the Coriolis force that breaks Galilean invariance and opens a gap at low frequency. I will explore how the number and spatial profile of topological edge states depends on an anomalous response coefficient called odd (or Hall) viscosity. As the sign of odd viscosity changes, a topological phase transition occurs without closing the bulk band gap. For large odd viscosity, this transverse response can be measured via the profile shape of topologically robust edge waves.