Impurities control phase stability and phase transformations in natural and man-made materials, from shape-memory alloys(1) to steel(2) to planetary cores(3). Experiments and empirical databases are still central to tuning the impurity effects. What is missing is a broad theoretical underpinning. Consider, for example, the titanium martensitic transformations: diffusionless structural transformations proceeding near the speed of sound(2). Pure titanium transforms from ductile a to brittle. at 9 GPa, creating serious technological problems for beta-stabilized titanium alloys. Impurities in the titanium alloys A-70 and Ti-6Al-4V (wt%) suppress the transformation up to at least 35 GPa, increasing their technological utility as lightweight materials in aerospace applications. These and other empirical discoveries in technological materials call for broad theoretical understanding. Impurities pose two theoretical challenges: the effect on the relative phase stability, and the energy barrier of the transformation. Ab initio methods(4,5) calculate both changes due to impurities. We show that interstitial oxygen, nitrogen and carbon retard the transformation whereas substitutional aluminium and vanadium influence the transformation by changing the d-electron concentration(6). The resulting microscopic picture explains the suppression of the transformation in commercial A-70 and Ti-6Al-4V alloys. In general, the effect of impurities on relative energies and energy barriers is central to understanding structural phase transformations.