In HEAs, as in conventional alloys, phase instabilities can have beneficial or harmful effects on mechanical properties. For example, in HEAs with the FCC structure, a latent tendency for transformation to HCP anticipates twinning and/or transformation induced plasticity (TWIP/TRIP), which can enhance strength and ductility. TRIP effects have been reported also in some BCC refractory-metal HEAs. In both structures, alloy compositions can be tuned to control phase stability and, in turn, mechanical properties. Another kind of transformation occurs in single-phase HEAs most of which are actually metastable. They decompose into their thermodynamically stable phases during intermediate-temperatures anneals once nucleation and growth barriers have been overcome. Severe embrittlement is often the result, as has been shown in both FCC and BCC HEAs. In this talk I will use model HEA systems to highlight fundamental aspects of these two types of phase instabilities and their effects on mechanical properties.