The Gaussian expansion method and its application to various three-, four-, and five-body problems are reviewed. As examples for the application, we review i) the application to three- and four-body 4He-atom clusters and ii) benchmark testing for four-nucleon bound states using realistic force and calculation of the second 0+ state of 4He, iii) the four-body calculation of 4 H and 4He taking N- coupling, and iv) the five-body calculation of a double hypernucleus, 11 Be. In addition, we discuss the understanding of the structure and the mechanisms of those systems together with some useful techniques for the calculations. We obtain the first numerically reliable solution to the binding energies and wave functions of the four-body system of 4He atoms interacting with an extremely strong short-range repulsion and a weak van derWaals attraction. By applying the method to the calculations of the four-nucleon bound state, we find that the drastic change in the spatial structure between the 0+ 1 to 0+ 2 states is well understood in terms of the GEM four-body calculation. The four-body calculations are performed for 4 H and 4 He and the role of conversion in these hypernuclei is discussed. Energy levels of the double hypernucleus, 11 Be, are calculated within the framework of an ααn five-body model. The Hida event, recently observed in the KEK-E373 experiment, is interpreted as an observation of the ground state of 11 Be.