The algebras of higher spin symmetries in conformal field theories in four and six dimensions are not unique and have a richer structure due to the existence of infinite short multiplets besides the usual scalar and spinor. We will focus on recent results that show there exists a one parameter family (continuous of d=4 and discrete for d=6) of higher spin algebras and superalgebras, and give an explicit unitary representation for these algebras using quasiconformal methods. We will also discuss the implications of these results for the AdS5/CFT4 and AdS7/CFT6 higher spin holography.