In this talk we will explain how the determination of the scaling limit of parafermionic observables can be used to deduce the conformal invariance of interfaces in planar random-cluster models with cluster-weight 1 ≤ Q ≤ 4 (1\leq Q \leq 4). The strategy was introduced in the context of the loop-erased random walk by Lawler-Schramm-Werner, and was implemented for the FK Ising model (a.k.a. the random-cluster model with cluster-weight equal to 2) by Chelkak, Duminil-Copin, Hongler, Kemppainen and Smirnov, based on a main contribution of Smirnov.