Metamaterials are composites consisting of artificial meta-atoms/ metamolecules with typical sizes less than the wavelength of operation. One of the key properties that makes metamaterials distinctly different form the natural media is a very strong magnetic response that can be engineered in the visible and infra-red part of the spectrum. In this work we summarize our multipole expansion approach that can be used to describe analytically optical properties of metamaterials composed of, in particular, the split-ring and cut-wire resonators. An important feature of our formalism is the possibility of describing nonlinear response of a metamaterial, such as second harmonic generation, which arises due to induced high-order multipoles. Our model has recently been extended to the case of hybrid metamaterials composed of plasmonic nano-resonators coupled with quantum elements (such as quantum dots, carbon nano tubes etc). It has also been shown that apart from metamaterials various other physical systems can be successfully modelled within framework of the developed approach. For example, transient dynamics and steady-state regime of a nano-laser, as well as its stochastic properties (e.g. linewidth of generation) have been described using this model.