Exact results are obtained for two‐dimensional Ising models in which periodic conflicting interactions induce frustration effects. A brief review of the remarkable thermodynamic and magnetic properties of these models is presented. For specific choices of the interactions, the main features predicted are: (1) The existence of systems with a highly degenerate level of lowest energy, leading to a residual 0K entropy per spin. (2) According to the distribution of interactions, the existence of a residual 0K entropy is not an impediment to the onset of long range order at finite temperatures. However, if such an order takes place, the corresponding order parameter may not be saturated at 0K, and the associated susceptibility will diverge at 0K as well as at the transition temperatures. (3) Long range spin correlations ⟨S(O&vec;)S(R&vec;) ⟩ at 0K averaged over all ground states are studied in one of the models (which includes the ’’odd model’’) for simple crystallographic directions of R&vec;. They are shown to decrease as f (R&vec;) ⋅R−1/2where f (R&vec;) is an oscillatory factor, proper to each R&vec; direction, which results in marked anisotropy effects.