Solid-state amorphization of a crystalline solid to an amorphous phase is extensively studied as a first order phase transition at low temperature for almost thirty years. In this dissertation, we report the recent progress on phenomenological models employed for thermodynamic description of macroscopic systems and fluctuations and nucleation of mesoscopic inhomogeneous systems in binary solid solutions under polymorphic constraints with no long-range diffusion involved. Based on our understanding on atomic picture of solid-state amorphization in binary solid solutions, we propose a Landau free energy to describe amorphization as the first order phase transition. The order parameter is defined which represents the loss of long-range translational order. The elastic strain field induced by composition disorder plays the important role through the bilinear coupling with the order parameter. Elastic softening and amorphization happen simultaneously. From the similarity between the melting and amorphization, we use the temperature and composition as two external variables and treat solid-state amorphization as low temperature melting under polymorphic constraints. For homogeneous system, the phase diagrams for endothermic melting and exothermic melting are built separately and the corresponding thermodynamic quantities are presented. A microscopic homogeneous nucleation mechanism is proposed conceptually in binary solid solutions under polymorphic constraints. The formation of an amorphous embryo is initiated from the composition modulation in the crystal state and a subsequent polymorphous nucleation within the as-formed heterophase fluctuation. This homogeneous nucleation path is thought to be associated with the nonlinear energy localization mechanism connected with the localized large-amplitude excitations of atoms, which are induced by nonlinear and disorder. A Landau-Ginzburg free energy is constructed to describe the critical nucleus and the growth of the new phase in one-dimensional systems. Analytical and numerical methods contribute to the understanding the fluctuations and nucleation processes. Size-dependent melting and amorphization in nanosolids are investigated. Two models are proposed for nanocrystalline solid solutions to glass transformations. Based on the thin film model with finite thickness, we build one-dimensional Landau-Ginzburg approach, which includes surface contribution and size dependence, and numerical results do show similarity with experimentsâ results qualitatively.