First-order phase transformations, as typified by the martensite reaction, are being examined. The interrelation of discrete dislocation and nonlinear continuum diffuse interface models of interfacial core structure is investigated theoretically and experimentally in model martensitic systems. A nonlinear nonlocal continuum theory explores the competition between nucleation and continuous modulation modes of first-order transformations. Transmission electron microscopy investigation of ferrite interfaces assists in defining the interfacial structure. Homogeneous nucleation experiments are performed in submicron austenitic particles, using high magnetic fields to supply additional thermodynamic driving force.