In electromagnetism and fluid dynamics it is common to use formulations in terms of potentials, such as the magnetic vector potential, which leads to a problem for the curl-curl operator. In this kind of problems the solution is in general not unique, since adding any irrotational function to our solution will give another valid solution. It is then necessary to add a gauging condition to recover uniqueness. Tree/cotree gauging is a very efficient technique used in finite elements for gauging. It is based on creating a spanning tree on the mesh, i.e., a chain of edges that passes through every vertex of the mesh, without creating closed loops. The cotree is then formed by all the edges of the mesh that do not belong to the tree, and the solution of the curl-curl problem in the space generated by the cotree is unique. The main advantage with respect to other gauging techniques, such as imposing a zero divergence, either by penalty or through a multiplier, is that it reduces the size of the linear system and the associated matrix is symmetric and positive definite. It has been shown that, based on the existence of commutative isomorphisms between spline spaces and low order finite elements, the tree/cotree decomposition can be applied in IGA without effort, using the same algorithms existing for FEM. In this talk I will present recent advances in the generalization of the tree/cotree techniques for hierarchical splines, and for domain decomposition methods.