In this talk, we will give some recent results concerning property $T$ of $C^*$-algebras. 

In particular, for a locally compact group $G$，the full group $C^*$-algebra of $G$ has strong property $T$ if and only if $G$ has property $T$. 

Moreover, if $G$ is an $[IN]$-group, then the reduced group $C^*$-algebra of $G$ has strong property $T$ if and only if $G$ has property $T$.

Examples of non-property $T$ locally compact groups with their reduced group $C^*$-algebras having strong property $T$ will be given. 

An equivalent description of strong property $T$ of the crossed products of actions of locally compact groups on $C^*$-algebras that satisfies some conditions will also be presented.