Different phenomena that occur in a periodic array of plasmonic nanostructures are investigated in terms of periodicity and multipoles. In this presentation, we revisit the resonances that exist in periodic plasmonic systems, Fig. 1. Starting with some basic concepts such as the difference between Wood and Rayleigh anomalies, as well as the influence of the surrounding medium, we move to more advanced concepts, such as bound state in the continuum – which are receiving significant research interest today – and also the Kerker effect that can control absorption in the system and its scattering in specific directions. All these effects are associated with the excitation of multipolar surface lattice resonances and studying the evolution of these resonances as a function of the different geometrical parameters provides significant insights into the underlying physics [1]. These phenomena are also closely related to Fano resonances, since they stem from the interaction between different modes in the system, leading to an asymmetric lineshape [2]. Especially for bound states in the continuum, their very sharp spectral features stem from the interaction with propagating modes, which can be lattice resonances or guided modes. The latter echo strongly with the field of resonant waveguide gratings, which flourished almost fifty years ago [3]. Finally, we will show that these resonances do not only influence the linear behaviour of the system, but also its nonlinear response. For example, the strong absorption produced by the Kerker effect at the fundamental frequency can enhance the generation of second harmonics.