We present some aspects of the rheology of field-responsive suspensions, a class of field-responsive liquid-matter systems possessing the ability to undergo significant changes in their strength upon application of an external field. Both the single-particle and the many-particle domains are discussed. In the former, consideration of the full non-linear dynamics of the particles leads to an anomalous behaviour of the viscosity whereas in the latter the most salient feature is the formation of chains and fractal structures. We indicate how to deal with the rheology at moderate concentrations, leaving open the problem at higher concentrations for which the complexity of the emergent structures strongly limits the knowledge of their dynamics.