Abstract: This talk will be about newforms of representations of local unitary groups. Newforms were first studied by Casselman in the case of GL(2) and later generalized by Jacquet, Piatetski-Shapiro, and Shalika to GL(n). Recently, Atobe, Oi, and Yasuda defined and studied newforms for odd unitary groups and Atobe studied those for even unitary groups. We gave another definition of newforms for unitary groups and showed that under our definition newforms give rise to test functions of some local spherical character. In this talk we will compare these two definitions and introduce the local Langlands correspondence along the way. If time permits, I will also briefly talk about the Gan-Gross-Prasad conjecture and how it is used in our proof.