CAD models describe surfaces using a collection of patches that meet in curves and points. Ideally, the CAD surface is watertight, but there are often gaps or overlaps between neighboring patches. These gaps/overlaps may cause serious meshing and finite element analysis problems, and in practical applications, the CAD model often needs to be corrected before meshing is possible. This talk presents a robust CutFEM for handling CAD surfaces with gaps/overlaps; see [1]. The main idea is to cover the gaps/overlaps with a three-dimensional mesh and then use a hybrid variable on this mesh together with a Nitsche-type formulation. The hybrid variable transfers data between neighboring patches, and there is no direct communication between the patches. The hybrid variable must be given enough stiffness in the directions normal to the interface to obtain a convergent method. We show this can be done by adding a suitable term to the weak statement. We allow trimmed patches and add appropriate stabilization terms to control the behavior of the finite element functions in the vicinity of the trimmed boundaries using techniques from CutFEM, see [2]. In practice, we suggest an Octree mesh for setting up the hybrid mesh to facilitate efficient computation of the involved terms. We allow standard conforming finite element spaces and spline spaces with higher regularity. We derive error estimates and present several numerical examples illustrating the method's convergence and application to a realistic CAD model.