Much of the recent rigorous progress on the classical Ising model was driven by a new detailed understanding of its stochastic geometric representations. The extent of couplings between the Ising model and its FK, random current and high-temperature representations is ever-increasing. A framework unifying the relations will be presented, along with some surprising implications including:Percolation of the uniform even graph is not monotone in the domain.Percolation of the high-temperature expansion and single current is not monotone in the parameterAbsence of exponential decay for the random current corresponding to a supercritical Ising model.