A set of points $M$ of a finite polar space $\mathcal{P}$ is called tight, if the average number of points of $M$ collinear with a given point of $\mathcal{P}$ equals the maximum possible value. In the case when $\mathcal{P}$ is a hyperbolic quadric $Q^+(2n+1,q)$, 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 $Q^+(5,q)$. 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 set of hyperbolic quadrics.