In Fuzzy Cognitive Map based modelling, the final conclusion is based on the assumption that the system reaches an equilibrium point (fixed point) after a certain number of iteration. It is not straightforward that this leads to a fixed point, since the iteration may show various dynamical behaviours: multiple fixed points, limit cycle and unpredictable patterns may also occur. In this chapter, a gentle insight into the dynamics of FCMs’ is provided based on solid mathematical tools. We prove sufficient conditions for the existence and uniqueness of fixed points for sigmoid, hyperbolic tangent and rescaled sigmoid FCMs, which are also necessary in the case of the latter two. Additionally, symmetrical properties of fixed points and basins of attraction of hyperbolic tangent and rescaled sigmoid FCMs are also introduced with mathematical proof.