Results on asymptotic multimodal systems derived to describe resonant sloshing in clean two-dimensional rectangular tanks excited with the forcing frequency close to the lowest natural sloshing frequency are systematically reviewed. A focus is on steady-state (periodic) solutions of these systems whose behaviour demonstrates typical features of complex dynamical systems, e.g., multi-stability, bifurcations, and chaos appearing in certain forcing frequency domains. Derivation of the multimodal systems utilises a Miles-Lukovsky–type variational technique, which reduces the original free-surface boundary value problem to an infinite–dimensional system of ordinary differential equations coupling the generalised hydrodynamic coordinates and velocities of the hydrodynamic system, as well as asymptotic properties of the nonlinear resonant liquid sloshing dynamics. Using the asymptotic properties makes it possible to reduce the multimodal analysis to finite dimensions. The present review reports details on how to derive and study the corresponding finite-dimensional asymptotic modal systems consequently considering the Moiseev third-order asymptotics, adaptive modal systems and the Boussinesq–type multimodal theory required for intermediate liquid depths.