During the last decade, important attention has been devoted to the observation of nonlinear optical processes in plasmonic nanosystems, giving rise to a new field of research called nonlinear plasmonics. The cornerstone of nonlinear plasmonics is the use of the large field enhancement associated with the excitation of localized surface plasmon resonances to reach high nonlinear conversion yields. Among all the nonlinear optical processes, second harmonic generation (SHG), the process whereby two photons at the fundamental frequency are converted into one photon at the second harmonic frequency, is undoubtedly the most studied one due to the relative simplicity of its experimental observation. However, the physical origin of SHG from plasmonic nanostructures hides a lot of subtleties, which are mainly related to its particular behavior upon inversion symmetry. In order to catch all the peculiarities of SHG, it is mandatory to develop dedicated numerical methods able to accurately describe all the underlying physical processes and the influence of the initial assumptions needs to be well-characterized. In this presentation, we discuss and compare different methods (namely full-wave computations based on the surface integral equations method, mode analysis, the Miller’s rule, and the effective nonlinear susceptibility method) proposed for the evaluation of the SHG from plasmonic nanoparticles emphasizing their limitations and advantages. In particular, the design of double resonant antennas for efficient nonlinear conversion at the nanoscale is addressed in detail.