Level set models are deformable implicit surfaces where the deformation is controlled by a speed function in the level set partial differential equation (PDE). These models are widely used in computer graphics applications due to their implicit definition, low-level volumetric representation and the powerful numerical techniques used to produce the PDE-based deformation. We present a set of interactive sketch-based level-set surface editing operators. These operators allow a user to sketch curves above or on a level-set surface in order to edit the surface's shape. Once the curves are sketched the surface interactively evolves to locally fit to the curves. A user may then modify the curves in order to refine the shape of the model. The mathematics, algorithms and techniques needed to implement numerous sketch-based level set modeling capabilities are described. The speed functions that produce the surface deformations within the context of solving the level-set PDE are detailed. Several examples are presented to demonstrate the flexibility and usefulness of the editing operators.