Most existing geometry processing algorithms use meshes as the default shape representation. Meshes, however, are hard to optimize for topology changes and usually require remeshing when undergoing large deformation. This paper instead proposes the use of neural implicit fields for geometry processing. Neural implicit fields can compactly store complicated shapes without spatial discretization. Moreover, neural implicit fields are infinitely differentiable, which allows them to be optimized for objectives that involve higher-order derivatives. This paper develops loss functions and architectures to perform shape filtering and deformation with neural implicit fields. We provide experimental results that showcase the applicability of neural implicit fields to these tasks.