Magnetic insulators provide a clean arena to study collective effects in solids since the nature of the agents – magnetic moments, as well as their interactions are generally well known. The interplay between the local (neighbor/cluster) and extended (semiclassical) degrees of freedom is typically manifested at the nanometer scale and is of notable fundamental and practical interest. Neutron scattering is an ideal tool to study these phenomena.  Within the confines of this talk I shall discuss several topics sharing this common thread: (1) A perturbation of locally strongly bound magnetic clusters often causes an extended magnetic order to appear. The extreme situation of this scenario happens when local clusters themselves display a nonmagnetic quantum singlet ground state. For example, in the case of Cu₂Te₂O₅X₂ (X=Cl, Br) – a magnetic order is observed with a peculiar set of excitations (notably a weak Goldstone mode) measured by inelastic neutron scattering (INS). (2) In some insulators with a homogeneous spin lattice but a lack of inversion symmetry (i) a large-scale Skyrmion lattice ground state and (ii) magnetoelectric coupling appear. I shall describe the first successful attempts to control this type of structure by an electric field and measure the observed change by small angle neutron scattering (SANS). (3) In a homogeneous, but highly frustrated triangular spin lattice, there are emergent local excitations as contrasted to the normal long-range spin waves observed by SANS. Finally, (4) in selected finite magnetic systems (ferromagnetic magnetic molecules) one can consistently apply the methodology (ferromagnetic cluster spin-wave theory) developed for the extended systems in terms of exact calculation and visualization of INS observables. This turns out to be more than a theoretical device because precursors to spin waves in extended systems can indeed be observed by INS in large ferromagnetic magnetic molecules.