Consider a countable group G acting on the unit sphere S in the space of L^2 functions on G by the regular representation. Given a homology class h in the quotient space S/G, one defines the spherical Plateau solutions for h as the intrinsic flat limits of volume minimizing sequences of cycles representing h. In some special cases, for example when G is the fundamental group of a closed hyperbolic manifold of dimension at least 3, the spherical Plateau solutions are essentially unique and can be identified. However not much is known about the properties of general spherical Plateau solutions. I will discuss the questions of existence and structure of non-trivial spherical Plateau solutions.