Strong geometrical frustration precludes conventional magnetic ordering.  A common outcome is a completely disordered spin-liquid state  at zero and at low temperatures.  Another interesting possibility is a partial breaking of spin rotational symmetry described by spin-tensor order parameters.  We shall discuss two examples of such unusual symmetry breaking.  The first model example is a classical Heisenberg antiferromagnet on a kagome lattice [1].  At low temperatures the order by disorder mechanism selects a submanifold of planar spin states which are described by non-zero octupole moments.  An interesting consequence of such a third-rank tensor order parameter is presence of various types of fractional vortices.  The second example is a system of weakly coupled spin-1/2 frustrated ferromagnetic chains [2].  The high-field transition from the saturated phase occurs via condensation of bound magnon pairs.  Such a condensate of is described by spin-nematic or second-rank tensor.  We develop analytical theory for the bose condensation into nematic state and argue that corresponding transition is realized in LiCuVO4.

[1] M. E. Zhitomirsky, Phys. Rev. B {78}, 094423 (2008).
 [2] H. Tsunetsugu and M. E. Zhitomirsky, in progress (2010).