In this talk, we will describe applications of so-called parafermionic observables. These observables pop up in several models of two-dimensional statistical physics. At criticality, they satisfy local relations which may be understood as discrete versions of Cauchy-Riemann Equations. Unfortunately, these local relations often provide partial information only on the behavior of the observables. We will explain how this partial information can still be used to prove a number of results, including the computation of the connective constant of the hexagonal lattice, and some inequalities on the critical point of the loop O(n) model.