Fluid deformable surfaces show a solid–fluid duality which establishes a tight interplay between tangential flow and surface deformation and can be modeled by (Navier-)Stokes-Helfrich equations. Starting from these equations and numerical approaches to solve them, we extend the model towards active surface nematodynamics (surface Beris-Edwards like models) and discuss various modeling and numerical issues. We demonstrate emerging shape instabilities and current research on the impact of nematic order and topological defects on shape evolution. This is joint work with Ingo Nitschke and Maik Porrmann.