Metal cutting and deformation processing operations provide some of the most challenging problems for modeling and simulation in computational plasticity. These challenges include, but are not limited to, extreme plastic deformation, challenges in constitutive and interfacial friction modeling, microstructural effects, mechanical and thermoplastic instabilities, multiphysics effects due to cutting fluid and high temperatures, and are generally computationally intensive. Despite considerable progress in each of these fronts, there is scope to expand the envelope of simulations that capture the deformation physics while being computationally feasible. Moreover, even conventional standard FEA codes can be leveraged for modeling and simulation in more effective ways. In this work, we present three challenging scenarios for modeling, namely large strain extrusion machining (LSEM), forming using a flat punch, and cutting of inhomogeneous metal, using a mix of Arbitrary Lagrangian Eulerian (ALE), conventional Lagrangian FE, and remeshing techniques. Some of these simulations are ‘standard’, while others are first-in-class, and we discuss both specific and general modeling issues that must be considered to obtain good quality solutions. Specific mechanics insights gleaned from each of these case studies are also presented, ranging from the influence of friction in deep punch indentation to the selection of the chip thickness ratio in LSEM. The last part of this work focuses on problems that arise in the simulation of polycrystalline aggregate cutting, and the progress made in addressing them.