The high temperature BCC phase (b) of titanium undergoes a martensitic transformation to HCP phase (a) upon cooling, but can be stabilized at room temperature by alloying with BCC transition metals such as Mo. There exists a metastable composition range within which the alloyed b phase separates into a + b upon equilibrium cooling but not when rapidly quenched. Compositional partitioning of the stabilizing element in as-quenched b microstructure creates nanoscale precipitates of a new simple hexagonal w phase, which considerably reduces ductility. These phase transformation reactions have been extensively studied experimentally, yet several significant questions remain: (i) The mechanism by which the alloying element stabilizes the b phase, thwarts its transformation to w, and how these processes vary as a function of the concentration of the stabilizing element is unclear. (ii) What is the atomistic mechanism responsible for the non-Arrhenius, anomalous diffusion widely observed in experiments, and how does it extend to low temperatures? How does the concentration of the stabilizing elements alter this behavior? There are many other w forming alloys that such exhibit anomalous diffusion behavior. (iii) A lack of clarity remains on whether w can transform to a -phase in the crystal bulk or if it occurs only at high-energy regions such as grain boundaries. Furthermore, what is the nature of the a phase embryo? (iv) Although previous computational results discovered a new wa transformation mechanism in pure Ti with activation energy lower than the classical Silcock pathway, it is at odds with the a / b / w orientation relationship seen in experiments. First principles calculations based on density functional theory provide an accurate approach to study such nanoscale behavior with full atomistic resolution, allowing investigation of the complex structural and chemical effects inherent in the alloyed state. In the present work, a model Ti-Mo system is investigated to resolve these fundamental questions. Particular attention is paid to how Mo- (i) influences the bonding in Ti, (ii) distorts the local structure in the Ti lattice, (iii) impacts the point and interfacial defect formation and migration energies, and (iv) affects the mechanism and energetics of b w and wa transformations. Our results are correlated with appropriate experimental results of our collaborators and those in open literature. The modification of Ti bonding by Mo solutes and the attendant distortion of the lattice hold the key to answering the diverse questions listed above. The solutes enhance electron charge density in the <111> directions and, consequently, stiffen the lattice against the displacements necessary for b w transformation. However, Ti atoms uncoordinated by Mo remain relatively mobile, and locally displace towards w lattice positions. This effect was further studied in a metastable Ti-8.3 at.% Mo system with an alternate cell geometry which allows for either b w or $\betaa transformation, and it was found that after minimization Ti atoms possessed either a or w coordination environments. The creation of this microstructure is attributed to both the disruption of uniform b w transformation by the Mo atoms and the overlap of Ti-Mo bond contractions facilitating atomic displacements to the relatively stable a or w structures in Mo-free regions. The vacancy migration behavior in such a microstructure was then explored. Additionally, several minimized configurations were created with planar interfaces between Mo-stabilized b region and its adjacent a- or w- phases, and it was found that the positioning of Mo at the interface strongly dictates the structure of the adjacent Mo depleted region.