The monodromy group of an IHS manifold is one of the most important tools to investigate their geometry. In the first part of the talk, I will recall the main definitions, giving some motivation. In the second half I will focus on the OG10-type. This is the only type (among the known ones) for which the monodromy group is still a mystery. We explain how to construct new monodromy operators using two families, the O'Grady and the Laza-Saccà-Voisin ones, exhibiting an explicit subgroup of the monodromy group, that we conjecture being all. Time permitting, we will also discuss a geometric constraint to the fact that the monodromy group is smaller than the group of orientation preserving isometries.