  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 nonlinear dynamics of the particles leads
to an anomalous behavior 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 moderately concentrations leaving open the
problem at higher concentrations for which the complexity of the emergent
structures strongly limits the knowledge of their dynamics.
