When simulating moving bodies using body-fitted meshes, the boundaries of the computational domain may undergo arbitrarily large deformations. In aerospace applications, typical examples include the deployment of aerodynamic surfaces, rocket booster or payload detachment, and flow past rotors or turbomachinery stages. Accurate representation of such motions is essential for the correct computation of aerodynamic forces. However, standard dynamic mesh methods that deform the grid while keeping the connectivity fixed may result in poor-quality or invalid meshes. Remeshing after a certain number of time steps is a possible alternative, but it requires interpolation between meshes, which may compromise conservation properties and solution accuracy. This talk discusses advanced strategies for handling large mesh deformations while avoiding, or significantly delaying, remeshing. The first strategy permits to describe local mesh adaptation, such as node insertion and removal, and edge swapping, within the Arbitrary Lagrangian-Eulerian (ALE) formulation. This approach avoids the need to interpolate the solution between successive meshes, thereby facilitating the implementation of multi-step time integration schemes Secondly, a novel sliding-mesh technique that preserves a conformal interface between rotating subdomains is presented. In standard sliding-mesh approaches, one subdomain rotates rigidly with respect to another without modifying the interface geometry. When the interface is discretized using planar (in 3D) or linear (in 2D) elements, relative motion leads to gaps or overlaps at the interface, undermining numerical conservation. The proposed method restores a conformal interface at each time step, eliminating gaps and overlaps. This result paves the way for treating sliding-mesh techniques within the ALE framework.