What is the price of naturalness? In minimal extensions of the standard model, stringent limits on new colored particles and measurements of Higgs properties from the LHC severely challenge the hypothesis of naturalness of the electroweak scale. However, these measurements also provide unprecedented guidance in exploring non-minimal models of new electroweak physics. The supersymmetric twin Higgs provides a concrete example where few-percent level tuning remains compatible with superpartner limits and Higgs physics as well as gauge coupling unification and other successes of the MSSM. Studying such models in detail is crucial to understanding the role naturalness will play as a motivating principle for future searches at the 13 TeV LHC and beyond.