In recent decades, there has been a lot of interest in geometrically frustrated systems. The term "geometrical frustrations" refers to situations where local order, as determined by local interactions, cannot freely propagate throughout the space, and the long-range order cannot be established. Instead, a highly degenerate ground state is formed. Interest in these systems stems from (i) the richness of their novel properties: the unexpected variety of ordered states and transitions between them; (ii) the complexity of the underlying physics: the close coupling and correlations among spin, orbital, charge and lattice degrees of freedom; (iii) the presence of frustration that makes the systems highly sensitive to any internal or external perturbations.

The pyrochlore lattice, which is composed by corner sharing tetrahedra is a typical example of a highly frustrated three dimensional structure. It is believed that Heisenberg antiferromagnet on a pyrochlore structure does not support a magnetically ordered ground state. Often in real systems, for example, in spinels, with the general formula AB$_2$0$_4$, a magnetic ion can also possess an orbital degeneracy in addition to the spin one. the physical behavior of such systems may be drastically different from that of pure spin models, as the occurrence of an orbital ordering can lift the geometrical degeneracy of the underlying lattice. As an example, I will discuss three compounds with such properties: the B-spinels LiV204, MgTi204, and ZnV204.