I will explain the notion of a homotopy quotient of an operad providing different examples of operads of compactified moduli spaces of genus zero curves with marked points: including the space of complex curves (math.arXiv:1206.3749), the real loci of the complex one (arXiv:math/0507514) and the noncommutative one (math.arxiv:1510.03261). As a conclusion I will suggest a description of the rational homotopy type of $\bar{M_{0,n}(R)$ and show that this manifold is not formal (work in progress with T.Willwacher).