A fascinating class of problems in contemporary fluid mechanics involves the interplay between dynamic boundaries and fluid flows. The study of these problems usually requires accommodating several time and length scales. Moreover, they often involve complex geometries in which mechanical, chemical, and transport phenomena are coupled. The multi-scale, multi-physics nature of such problems makes it extremely challenging to develop comprehensive analytical models for treating these systems. Also, experimental approaches are typically very costly, time-consuming, and require significant effort unless guided by theory or simulations.