Phase transitions play a fundamental role in natural and industrial processes, yet predicting how phase boundaries evolve over time remains difficult. While thermodynamics captures equilibrium states, the transport of heat and chemical species, often amplified by fluid motion, governs the progression of phase change. Consequently, the book centers on the interaction between fluid flow and solid phase transitions, including melting, solidification, and chemical reactions such as dissolution and precipitation, each presenting unique challenges. From the melting of ice and glacier evolution to the formation of karst landscapes by rock dissolution, the coupling of flow, topography, and phase change drives pattern formation across diverse natural systems. These processes also shape groundwater dynamics and mineralization in porous media. Beyond environmental and geophysical settings, similar mechanisms underpin applications in hydrology, thermal sciences, and metallurgy. Bridging theoretical foundations, experiments, and numerical methods, this volume provides a comprehensive framework for understanding phase transitions in flowing systems for researchers, engineers, and graduate students.