I discuss the implications of the 126 GeV Higgs boson discovery for natural extensions of the Standard Model. In composite Higgs models, light fermionic top partners often play a role in obtaining a light Higgs mass. These are typically accompanied by massive gluon partners which can contribute sizeable radiative corrections to the Higgs mass, thereby easing the tension of having a light Higgs with heavy top partners. On the other hand if the Higgs is elementary, supersymmetric models with light stops and gluinos require new contributions to the Higgs mass. In the NMSSM with a large singlet-Higgs coupling this relieves the usual tuning in the Higgs vacuum expectation value. However, new sources of tuning from the Higgs mass and the Higgs couplings further constrain the naturalness of the model, implying that the natural region of NMSSM parameter space will be fully explored during Run-II of the LHC.