Twin Higgs models give a concrete realization of the so-called "Neutral Naturalness" paradigm, where no new light colored states are necessary to stabilize the electroweak scale. After a review of the basic Twin Higgs mechanism, I will discuss supersymmetric UV completions and their model building issues. I will show that many features of Twin SUSY models such as the Higgs mass constraint and the electroweak symmetry breaking conditions can be discussed in a largely model-independent way. This analysis can be used to identify new promising models with small fine-tuning and distinct phenomenology.