Two-layer flows are found in both nature and industry, e.g. coating, co-extrusion. At certain operating conditions, wavy interfaces, also known as instabilities, are observed in the flow that affect the quality of the final products. A long-standing problem has been how to design the process simply in a way that remains faithful to the flow stability. Although resolved for single fluid flows around 10 years ago, extending this methodology to multi-fluid flows has been evolved more slowly owing to the difficulties associated with the interface between the fluids. In this book, these flows have been studied from a mathematical modeling perspective. The models developed and their implementation to a two-layer system enable us to predict the behavior of co-extrusion and coating flows more accurately, allowing us to prevent defects in the final products due to the flow instability.