A set of points M of a finite polar space P is called tight, if the average number
of points of M collinear with a given point of P equals the maximum possible value.
In the case when P is a hyperbolic quadric, the notion of tight sets
generalises that of Cameron-Liebler line classes in PG(3,q), whose images under the Klein
correspondence are the tight sets of the Klein quadric. Very recently, some new constructions
and necessary conditions for the existence of Cameron-Liebler line classes have been obtained.
In this talk, we will discuss a possible extension of these results to the general case of tight sets
of hyperbolic quadrics.