One of the most efficient approaches to design the properties of a material is through the control of its phase transformations and microstructure evolution. The processes involved in a phase transformation are inherently multiscale. It starts with the nucleation of nanoscale nuclei of new phase particles, followed by growth and particle impingement or coarsening. In our recent works, we have developed a computational tool based on the phase-field description to predict the morphology of critical nuclei in solids under the influence of both interfacial energy anisotropy and long-range elastic interactions. Examples include cubic to cubic and cubic to tetragonal transformations. It is demonstrated that the morphology of critical nuclei in cubically anisotropic solids can be efficiently predicted without a priori assumptions. It is shown that strong elastic energy interactions may lead to critical nuclei with a wide variety of shapes including plates, needles, and cuboids with non-convex interfaces.