  Different types of order are discussed in the context of strongly correlated
transition metal oxides, involving pure compounds and $3d^{3}-4d^{4}$ and
$3d^{2}-4d^{4}$ hybrids. Apart from standard, long-range spin and orbital
orders we observe also exotic non-colinear spin patterns. Such patters can
arise in presence of atomic spin-orbit coupling, which is a typical case, or
due to spin-orbital entanglement at the bonds in its absence, being much less
trivial. Within a special interacting one-dimensional spin-orbital model it is
also possible to find a rigorous topological magnetic order in a gapless phase
that goes beyond any classification tables of topological states of matter.
This is an exotic example of a strongly correlated topological state. Finally,
in the less correlated limit of $4d^{4}$ oxides, when orbital selective Mott
localization can occur it is possible to stabilize by a $3d^{3}$ doping
one-dimensional zigzag antiferromagnetic phases. Such phases have exhibit
nonsymmorphic spatial symmetries that can lead to various topological
phenomena, like single and mutliple Dirac points that can turn into nodal rings
or multiple topological charges protecting single Dirac points. Finally, by
creating a one-dimensional $3d^{2}-4d^{4}$ hybrid system that involves orbital
pairing terms, it is possible to obtain an insulating spin-orbital model where
the orbital part after fermionization maps to a non-uniform Kitaev model. Such
model is proved to have topological phases in a wide parameter range even in
the case of completely disordered $3d^{2}$ impurities. What more, it exhibits
hidden Lorentz-like symmetries of the topological phase, that live in the
parameters space of the model.
