Abstract: Chirality ("handedness") of electron spins is a hallmark of many systems of current interest, including two-dimensional electron gases (2DEG) in semiconductor heterostructures, surface (edge) states of topological insulators, and graphene (in the last example, it is a pseudo- rather than real spin which is chiral). While by now we know a lot about single-particle properties of these systems, their many-body properties are just starting to be explored. In this talk, I will discuss a general phenomenology of non-SU(2) invariant Fermi liquids. The main prediction of the phenomenological approach--complemented by a microscopic calculation--is the existence of a new type of collective modes: "chiral spin waves", which we propose to observe experimentally in a semiconductor hetetorostructure with an in-plane modulation of the spin-orbit interaction. I will also discuss how spin-orbit interaction affects the non-analytic corrections to the Fermi-liquid behavior. In particular, a non-analytic dependence of the spin susceptibility on the momentum is shown to result in a new type of long-range RKKY interaction between localized moments embedded into a 2DEG, with a period given by the spin relaxation length rather the Fermi wavelength.