The understanding of disorder has profoundly influenced the development of condensed matter physics, explaining such fundamental effects as, for example, the transition from ballistic to diffusive propagation, and the presence of quantized steps in the quantum Hall effect. For superconductors, the response to disorder reveals crucial information about the internal gap symmetries of the condensate, and thereby the pairing mechanism itself. The destruction of superconductivity by disorder is traditionally described by Abrikosov-Gorkov (AG) theory, [1,2] which however ignores spatial modulations and ceases to be valid when impurities interfere, and interactions become important. Here we study the effects of disorder on unconventional superconductors in the presence of correlations, and explore a completely different disorder paradigm dominated by strong deviations from standard AG theory due to generation of local bound states and cooperative impurity behavior driven by Coulomb interactions. Specifically we explain under which circumstances magnetic disorder acts as a strong poison destroying high-T c superconductivity at the sub-1% level, and when non-magnetic disorder, counter-intuitively, hardly affects the unconventional superconducting state while concomitantly inducing an inhomogeneous full-volume magnetic phase. Recent experimental studies of Fe-based superconductors (FeSC) have discovered that such unusual disorder behavior seem to be indeed present in those systems.For cuprates, heavy-fermions, and FeSC the study of disorder currently constitutes a very active line of research, motivated largely by the fact that these systems are made superconducting by "chemical disordering" (charge doping), but also boosted by controversies of the correct microscopic model, and a rapid development of local experimental probes. [3][4][5] Focusing on multiband FeSC, disorder studies have proven exceptionally rich and strongly material dependent.[6] Scanning tunneling spectroscopy found a plethora of exotic atomicsized impurity-generated states, [7][8][9][10] NMR and neutrons observed clear evidence of glassy magnetic behavior, [11,12] and µSR discovered magnetic phases generated by non-magnetic disorder. [13,14] The resulting complex inhomogeneous phases and their properties in terms of thermodynamics and transport constitute an important open problem in the field.Here, we present a theoretical study of correlationdriven emergent impurity behavior of both magnetic and nonmagnetic disorder in unconventional s± multi-band superconductors. For the case of magnetic disorder, we find that correlations anti-screen the local moment, and significantly enhance the inter-impurity RudermanKittel-Kasuya-Yosida (RKKY) exchange interactions by inducing non-local long-range magnetic order which operates as an additional competitor to superconductivity. This results in an aggressive T c suppression rate where superconductivity is wiped out by sub-1% concentrations of disorder. This mechanism explains the "poisoning effect" discovered in ...