A review of different variational expansions most common in atomic physics is given. It will be shown that the exponential expansion with randomly chosen parameters seems the most universal one and with equal success can be applied to atomic and molecular systems and high angular momentum states. The further stage in precise studying of atomic and molecular spectroscopy is higher order relativistic and QED corrections. It is advocated that the most suitable background for that is an effective field theory called the non-relativistic QED (NRQED). A lot of numerical results, which demonstrate a power of the developed methods, will be presented.