The materials that exhibit martensite transformation have very important applications in engineering, and the microstructures of the materials play a key role foraffecting their mechanical behavior in macroscope. Therefore many attentions havebeen drawn for studying the related problems. This work focuses on the motion oftwin boundaries. Three questions are being asked: how is a twin boundary is nucleated in a homogenous (untwinned) material? After the twin boundary is nucleated,how is its motion initiated? How fast does it move? This study provides an atomisticunderstanding for these three questions. Linear stability analysis is firstly applied to capture the initiation of motion of atwin boundary. When a twin boundary is about to move, the lowest eigenvalue of thesystem Hessian drops to zero. And the corresponding eigenvector predicts accuratelythe way in which the twin boundary is going to move. The same idea is applied toinvestigate how motion of an irrational twin boundary is initiated. Atomic modelsof irrational twin boundaries are constructed by employment of continuum models,provided that the point group of rotations which relate two variants is extended toany rotations in plane. The zero eigenvectors reveal the complicated behavior ofmotion of irrational twin boundaries. The problem of nonuniqueness of kinetic relations proposed by Schwetlick andZimmer is solved in a thermoelasticity framework. By calculating the net heat fluxcrossing the phase boundary which is carried by the phonons, a unique kinetic relationcan be determined. Finally, a nonlocal criterion for nucleation of twin boundariesis proposed. By checking the stiffness of each unit cell evaluated with respect to asingle variable that represents the displacement along the unit cell diagonal direction,locations and the orientations of nucleated twin boundaries can be predicted.