This paper deals with the magnetic properties of some 1d systems isolated in solid state chemistry, and characterized by an exotic stacking of the magnetic ions (ladder-like, frustrated and trimerized chains). The thermodynamics (magnetic susceptibility, specific heat) and critical behaviors are shown to be very sensitive to the connections between metal ions, and the spin symmetries. The results are applied to experimental data for determining the relevant parameters in copper(II), cobalt(Il) and vanadyl(II) exotic chains.