We review some results concerning integrable systems on the moduli spaces of holomorphic bundles. The interrelations between bundles of different topological types are given by modifications (singular gauge transformations). The modification provides canonical maps between corresponding integrable systems. It also allows to describe the Backlund transformations. We apply the general scheme to the elliptic Calogero-Moser model and construct a map to an integrable Euler-Arnold top (the elliptic SL(N)-rotator). The models correspond to the bundles of degree zero and one. Explicit formulae represent a bosonization of the coadjoint orbit. The later describes the phase space of the rotator while the Poisson structure of the Calogero model is canonical. The construction can be generalized to more complicated models. For example, field generalization (loop group or 1+1 theories) leads to relation between the field Calogero model and the Landau-Lifshitz equation for XYZ model while the generalization to the isomonodromic deformations leads to relation between Painleve VI equation and Zhukovsky-Volterra gyrostat. In the end we note that the classification of models is described by the center of the structure group which are shown to be characteristic classes of the bundles. This remark allows to generalize the construction to the case of an arbitrary simple Lie group. Three-dimensional generalization of the construction naturally leads to the Bogomolny equations. The modification in this case provides non-trivial charge of the monopole solution. We find the Dirac monopole solution in the case (R)x(Elliptic curve). This solution is a three-dimensional generalization of the Kronecker series. We give two representations for this solution and derive a functional equation for it.